Water getting past your tile surface in the shower is not a problem. Indeed, it's quite normal. That's why we always provide a waterproof liner to direct such water to the drain in a properly constructed shower. Look in the Shower Construction section of our whirl-famous Liberry
to see how showers are constructed and you'll have a bit better insight into what you've got. The liner material may be much different in your shower, but the concept will be the same.
Water leaking beyond this liner is
a problem. Your liner has failed for one reason or another, which is not too surprising given its age.
The fix? Plan to do the replacement of this shower a bit sooner than you anticipated. Very unlikely you can do any sort of repair without replacing at least the lower foot or so of the shower, and it's equally unlikely the part above that is worth saving if you're going to the trouble to replace the bottom.
My opinion; worth price charge.