I am currently living in a older mobile home and rehabing it.
As posted by jazman, they cut every corner they can. Mine actually has 2x4 joist sitting on metal frame supports every 8' and 5/8" plywood on top.
Then some use the particle board and 2x6 joist.
Mine was gutted out and they added 3/4" cdx over the top to stiffen it up. I am still skeered to do tile.
Point is, they make these floors so cheap, tile job you describe, I bet they did not add hardibacker.
Obvious the tile needs to come up, If you can figure out what framing it has, stiffen up as needed, who knows, maybe hardibacker will be enough. Maybe you can add some support between the joist and stiffen it up. Then you have to deal with insulation on floor joist to get working room.
This can be done, will take creativity to tile a mobile home floor that will last.