Q: Tick in drivers side gets lower after warm up

In your initial question, I did not know that valve damage occurred as a consequence of a failed timing belt replacement. The 4 valves that the shop "claims" were damaged might merely represent what they "think" was the extent of the damage when the valve train interfered with the pistons during the failed timing belt replacement. The point is the noise that you are now hearing may represent damage from other segments of the valve train and indeed could have nothing to do with the 4 valves, or their lifters, that were claimed to be worked on. The bottom line in your circumstance is the ONLY way to identify the origin of the noise, that is describe the cause to you, is to disassemble the engine. I could list every cause of engine noise, or even the shorter list of "most" likely causes, and such would be meaningless and useless because the bottom line is, given what you are describing, the engine will have to be disassembled to repair the damage. And, given the circumstances you have described, at this point, the disassembly and repair will have to be performed by somebody who actually knows what they are doing and are capable of following instructions. If you still dealing with the shop that already damaged the engine, you will probably go from the frying pan into the fire. Some YourMechanic professionals are set up to perform complex engine repairs. My advice would be to see if an individual is available so you can obtain some rational resolution to this. As far as whether or not it is OK to continue to use the vehicle as is, nothing you have described suggests an urgent need to remove the vehicle from service.