I live in TX - does that make a difference?
No. The laws of negligence are relatively universal and I knew where you were when I responded.
could my condo association have a rule about this?
You would have to study your CC&Rs to find it. Your CC&Rs are a contract that you agreed to comply with when you bought your unit. If the CC&Rs hold you strictly responsible for the downstairs damage, well, that's that. On the positive side, I've read hundreds of CC&Rs as a claim rep, and I haven't seen one that has trumped negligence law. Make sure you read it, though.
I did fix the kitchen the day after they told me there was water stain downstairs.
Just understand that fixing a problem after being notified about it is NOT an admission or proof of negligence.
I plan on fixing the bathroom, of course. At the moment, no further water damage can occur because I don't let the water reach the overflow thing.
As long as you are sure you can prevent further damage you are OK.
I was worried about contacting my insurance because I do NOT want a mark with them!
That's up to you but you end up taking the risk that they deny the claim because of not reporting it and then you'd have to pay your own lawyer if you got sued.
I had to make a claim 6 months ago for jewelry, and I had a claim in 2004 and 2003. There was a gap between coverage for two years after 2004. When I started up my policy again, they upped my rates due to the prior claims !
Yes, and that could happen again.
if they fix their ceiling before my bathroom is fixed, and in the fixing their celing is damaged again, would I be liabe for that?
Yes, if your failure to repair the problem causes new damage or exacerbates the old damage.
The only reason I put it off if the bathroom needs complete remodeling. I have been saving up. I do not want to pay for the tile to be ripped up twice.
I am now in a position where I have no choice - it is just a matter of getting someone out here before they proceed with repairs in their unit
One option is to have the plumbing problem repaired from below since they have to cut out the damaged drywall anyway.