Bass tuner loose before catching

If I'm following you correctly, the worm has room to move around before engaging the gear. If you go strictly on what the pitch of the string does then the nut or other things could change things, but when the worm and gear are not engaged well you can generally feel it.

In theory, every tuner has some level of slop in there, it is just a matter of whether it is perceptible. This is part of why we were all told to detune and then tune up to pitch, even though we never knew why, and the person telling us to do it probably didn't either. It is common for it to be really obvious in old tuners. It'll stay in tune just fine, it is just annoying when you're trying to tune.

Some tuners can be improved if there is an adjustment screw (typically the one at the end of the button, sometimes at the opposite end) which draws up slack in the worm, usually against some sort of bushing. I really doubt that is the case on your bass. Lubricating it won't do anything to fix it, but can sometimes make it less annoying because it won't feel as strange when it finally engages.