2004 Hyundai Tiburon Timing belt

Yes. Your engine is an "interference" engine meaning if the timing belt breaks, any open valves will be hit by the pistons as they coast to a stop and will be bent. That turns a four-hour maintenance repair into a real expensive one. In the '80s Honda recommended replacing the timing belts every 75,000 miles, and they commonly broke at 65,000 miles resulting in a lot expensive repair bills. For that reason, I recommend not going by the interval spelled out in the owner's manual for any car brand. The only exception is for non-interference engines. For those, you risk needing a tow to a repair shop at the most inconvenient time, but not serious engine damage.

If a mechanic was trying to earn your business by giving you a lower estimate than his competitors, the belt can be replaced by itself, but that's like saying you CAN buy a new pair of shoes without buying the new shoe laces they normally come with. You could, but you wouldn't. When an experienced professional has your best long-term interest at heart, he is going to replace the water pump and any other pulleys with bearings, and any tensioning devices. When the water pump fails, the complete timing belt job has to be redone along with the additional pump and labor. Replacing both at the same time makes the most economic sense.

If any idler pulley develops a wobble due to a failed bearing, the belt will track off-center and will start to shred. That is avoided by replacing them at the same time as the belt. Since mechanics and parts suppliers realize the importance of having those parts in good condition, you will find most of those suppliers offer complete packages with everything included. Another advantage is you'll typically get a set of instructions included. When you buy an individual part, you'll need the manufacturer's service manual to find procedural steps and torque specs.

Some older engines use spring-loaded tensioner pulleys with a very low failure rate. Those are usually not replaced, but those are also on non-interference engines so if a bearing did go out, nothing other than the belt would be damaged. The risk is a lot higher with interference engines. Your tensioner is going to have to be removed and collapsed in a vise, then a pin is inserted to hold it there while everything is installed. Some of those tensioners just have a real strong spring inside that can break or get weak. Some are put under pressure with engine oil, and could develop a leak. As long as they have to be removed anyway to collapse them, it makes good sense to install a new one.

I use the Rock Auto web site for reference quite a bit. They have complete kits listed, but I see there are some that include parts that may need to be replaced when doing a valve job. You don't need all of those parts when just doing a maintenance belt replacement, but I would encourage you to consider replacing the water pump, pulleys, and tensioner.