Question 1: go ahead and reprocess it. Cranberry relishes are acidic enough that you would have been safe even if it wasn't in the fridge.

Question 2: No, you didn't cause it to seal. Sometimes, even though the vacuum has formed, lids don't ping. Touching them provides just enough give in the metal to react to the existing vacuum.

Since the relish is acidic, I would reprocess. If it had been left out, then, no, I would not have reprocessed if longer than 24 hours. If it were a low acid food, I would not reprocess, either. I would either eat that jar of food right a way or freeze it.
Sometimes if you touch the lids and they seal the come unsealed later in the pantry. Try to resist the urge and let them seal naturally.

I would reprocess. The 24 hr. rule is a good one. When I make salsa, sometimes I have much more than a canner full, so I cool down and refrigerate the extra and add it to my next batch at the end of the cooking, just to heat through.
I know it is tempting to check for a seal. Some take longer and you don't always hear a ping. If in doubt, mark the lid and use first. In your case, I would replace the lid as that may have been the problem.

How are the wedding plans coming along?! I get impatient too and will tap the top of my lids to see if they tink or thunk when I tap them. In the process, sometimes they Ping while I'm tapping (yes I know I sound ditsy!) I usually put those jars in the frig for immediate eating.

I'm sure this response is too late for your immediate question, but remember that if you have 10 jars of new stuff and add 1 jar of old stuff, then you have 11 jars of old stuff. If 'twere me, I'd keep that jar intact and reprocess with the batch.

Daughter's DH is constantly playing with the beautiful new jars when they come out of the canner, and he causes lots of no-seals. Best leave 'em alone! If they're going to ping, they'll get around to it. Some are just slow, that's true. Don't touch them until they're cool.

Leaving the threaded bands on until total cold, is one way to keep seals in tact. Usually the bands/rings should be screwed on tightly, but not as sight as commercially packaged products. Leaving them just a 'two finger tight' prior to going in the canner will cause more leakers. The contents should be as hot as possible when filling jars and if there is insufficient space at the tops (head space) the vacuum will be less. Many of my jars ping within just a few minutes after being taken out of the canner. When this occurs, I know that the batch has a good seal. Rarely do I ever have a bad seal, and can only recall a single quart of peaches that leaked. They were obviously bad as some of the liquid leaked out when fermentation may have occured, and the contents was down about 2 inches from where it should be. It was tossed, and after close examination of the jar, I found out that there was a small chip of glass missing from the sealing area. The lids do need to be in hot (not boiling) water so that the composite rubber will be soft and have the best chance of sealing once the lid has been screwed onto the jar using the threaded bands (rings). I prefer to leave the rings on until they are used. Some have rust problems, but I don't usually see that problem very much, especially because I use a hot wet sponge to clean the rims and threads before applying the lids and bands.