Hi,
The zone that you select in the zone restriction of shipping methods has to be either of the type "country", "state" or "shipping". If it's another type, it won't be taken into account.
Also, you can only select one zone in the restriction.
And the states, need to be published, and added as sub zones to that zone or it won't work.
Also, it needs to be the same state zones as the ones displayed for the state dropdown of the address. If you use other zones, the system won't be able to match them.
Finally, regarding UPS, if you don't get any results, it's either that the UPS plugin itself is not configured properly or that the products don't have a weight/dimensions setup. If you turn off the other shipping methods and only keep the UPS one, it will display an error message telling you why it can't display the UPS shipping methods.