Not quite understanding the issue here.
You mentioned NOT setting the TPMS, either with the "tool" or by one of the "learning" methods I've seen mentioned here, yet you are worried it's not working right?
Unused tool is a waste?
Some have posted that the system will eventually "learn" the new sensors by itself (on newer cars like yours) but I don't remember how long it took. (thinking it's a bit longer than you gave it)
Using one of the self-learning methods, or the TPMS tool, is the way to get it working right immediately AFAIK.