Yes, you need a plumber ASAP. Could be coming from a leaking toilet seal? Or traveling under the tile from another location. If you have shut-off valves in that room, I would turn them off.

This squish feeling means the subfloor below the tiles has been compromised/soaked with water and is now deteriorated to the point of "squishing". This requires a plumber and a bathroom fitter/installer once the plumbing has been corrected. I would hazard a guess that there is a leak somewhere in the walls/under the flooring. I would check the ceiling of the space BELOW the bathroom. If the water is affecting the floor in one space...it is probably affecting the ceiling/walls below as well.

Do you have home insurance? So long as this is a plumbing issue and not an installation issue, the home insurance should pay for it. Get insurance involved as soon as you can. That way you know what is going to be "out of pocket" and can set a budget accordingly.

Try to look on the bright side - if I'm right...you get a new bathroom!

Also, get started NOW! The insurance company will look at how fast you responded to the problem after you discovered it. Also the water may be getting into other rooms. Check the perimeters of all rooms that share a wall with this bathroom. If you find wet carpet, pull up the carpet and get fans going on it now. If it is very wet, hire a carpet cleaning service to come out and extract the water out of the carpet. What you do about tile or hardwood - I'm not sure! :)

Normally for insurance to cover the cost, it must be a gushing leak so you may turn up with no dice there. Did you purchase a home warranty? That may help as well.

Sounds like a leaking toilet. The subfloor is probably OSB with cement board on top which was not mortared down correctly so there is a floating pool between the surfaces. Your best bet is to call a bathroom remodeler that can do both plumbing and flooring... it may save on the end bill, ilo having multiple service companies tackle one problem.

I may add that home inspectors don't normally find all the problems, especially with toilet seals and such. You still may want to contact the home inspector though because they would surely stop out and take a look at things.

Inspectors put a clause in their reports that say this is what they found on this day, at this time so folks can't go back and say why didn't you mention this........ They also may exclude certain areas as being inaccessable, etc. ..............