As long as you have a temporary tag from one state, other states on your travels back to your home state will honor the temp tag. And, as long as you have all the proper paperwork - if you do get stopped, it’s very unlikely you’ll have any trouble.
It’s when your traveling away from your home state and don’t have the proper documentation that you need to be worried.
Ex: we bought a Jeep the end of May and got a temporary tag. We’re from Texas. In July we toaded it to New Mexico, Colorado, Utah and back, on a temporary tag. We were followed by law enforcement numerous times, whether while toading or driving around. Only had 1 instance that a local bleeped out on his intercom “no tag”, because Texas doesn’t issue 2 temporary tags - we only had 1 tag on the back.
He watched as we drove on, and then he saw the back tag. We continued on our merry way.
‘91 Ultrastar Champion‘02 Georgie Boy Landau 8.1l Workhorse
‘03 Jeep Wrangler TJ 2018 Jeep Wrangler JK toad