shut off engine it backpressure fills the expansion tank and pops the cap and dumps coolant?

It sounds like you have a blown head gasket even though there is no coolant in the oil which can happen. To confirm the issue a chemical test needs to be done.

Here is a guide that will help:

https://www.2carpros.com/articles/head-gasket-blown-test

and

https://www.2carpros.com/articles/recognizing-the-symptoms-understanding-a-blown-head-gasket-in-your-vehicle

Please go over these guides and get back to us.

I did the chemical test, 3 times at different times, it was negative, each time the results were the same as in the vid...also there is no misfire on any cylinder showing up with an OBD2 only code was for O2 sensor running lean, engine idles perfect. No bubbles in coolant either. No smoke. I have a 1998 Ford Taurus 3.0 Vulcan engine U VIN.

New water pump, new thermostat. 185 temp.

New expansion tank cap 16 psi

No combustion gases nor bubbles in the expansion tank per test.

No cylinder miss.

Mechanic says hoses are good

Radiator circulating and system flushed.

Fans work

Rusty water still even after flush. This is the 3rd time it's been flushed.

Only code showing is O2 sensor… lean.

After the engine reaches operating temperature and is driven for a few miles, the temperature begins to climb over normal range.

I never let it get beyond a hair over normal range.

Shut off engine the expansion tank steams and pops cap dumping engine coolant on ground.

I saw the TSB on this.

How do I know if a coolant bypass kit has been installed and is there any other reason this may happen? No mixing of oil and water.no vapor out the tailpipe.

No mixing of oil and water, no misfires showed up on an OBD2. The only code was for O2 sensor running lean...Engine idles perfect.no leaking anywhere, hoses good, new water pump, new thermostat. Radiator circulating fine according to the mechanic ...Combustion gas leak test done 3 times at different times. Vid shows results which were the same each time from cold start and even after being driven. No bubbles in expansion tank, no smoke nor vapor out tailpipe.
I reviewed all the links ..I have none of those symptoms. The only symptom is the coolant dump.

It seems that the thermostat was put in backwards by a mechanic in a reputable shop.
We bought another thermostat and pulled the old one videoed it..good cussing in it when we discovered the backwards thermostat. I will upload the vid so you can see, if language is not an issue. We properly installed the new thermostat. We are going to road test shortly and will let you know the results.

Thanks for the video. it does seem like the chemical was changing color slowly. This test is not 100% accurate and can produce a false negative. I think you may have a bad head gasket still, a very minor small leak but still enough to affect the engine overheating. Do the fans come on when the coolant reservoir is bubbling over? (Key on)

We took the chemical and put it in a bottle then blew through a straw into it ,it changed color after one breath two breaths changed it green, 4 breaths turned it yellow.. the test was preformed 3 times on that system with the same results each time and one of those tests were longer than 2 minutes and I agree I thought it maybe getting a lighter color. But really couldn't tell.

Fans do not come on when the dump of coolant happens because so far it only happens when you shut off the engine. But fans do come on when idling. Temp gauge will be showing normal operating temperature.
When you shut off the engine the coolant in expansion tank will slowly start to rise till it is full and you can hear it gurgling,then it spits it out.

After reinstalling the thermostat .we took a test drive with a lot of stops and starts and after about 15 minutes with the ac on, ....it's almost 90 here.... the temp gauge moved a hair above normal operating temp and I literally mean a hair above.. so I pulled over and shut it off it gurgled and dumped coolent..
We sat for about 15 minutes ,turned off a/c and refilled to lower mark on tank...cranked it up and drive without a/c for another 15 minutes..a lot of starts and stops...temp gauge sitting normal when i.pulled into my driveway. Turned car off.raised hood, Gurgling in the coolent system, water rising to the top of expansion tank till it overflowed but not as bad as when we had ac on.

Can you have a cracked cylinder head without a head gasket leak? Would it give the same symptoms as I am experiencing?

Yes, it would, the only other thing I can think of is the radiator is plugged internally so it would be difficult to see. Can I ask how you determined the radiator was clear? It could be plugged up externally as well. please check out this guide:

https://www.2carpros.com/articles/engine-overheating-or-running-hot

Please go over this guide and get back to us.

The expansion tank was being replaced for rupture. it had only been on for 5 months so shop said faulty part...we requested a system flush because of all the red slime mud that had been in the system when we purchased vehicle. The system has been flushed 2times in the past year. So, while they had it, we asked for a new water pump,a new thermostat a new radiator plus system flush.to remove any remaining stuff that maybe in the system.
The shop said we didn't need a new radiator cause radiator was circulating just fine and they felt we didn't need to spend that $700.00.

The problem will be either a partially clogged radiator or a blown head gasket.

It was a clogged radiator. brand new one put in 2days ago. It was the original radiator. Full of rust.
It fixed my problem. you couldn't see the stuff on the radiator through the grill. That "clean" area in the middle is all you could see when you looked through the grille.
Thank y'all.

Good find! Glad you could get it fixed, thanks for letting us know. Please use 2CarPros anytime we are here to help.