I'm not familiar with the Tetra Tint so I did a web search on their background. I found a site that said they were a cross between a Callifornia Gray rooster and a White Leghorn hen, so I made some guesses based on that. After Lilywhite's post I did some more searching and found a couple of sites that said they were a cross of RIR rooster over White leghorn hen.
Mt. Healthy Hatchery says they are RIR rooster over White leghorn hen, so I’ll go with that. If that is the case, the Tetra Tint would be split for Wheaton and Extended Black. I understand RIR are Wheaton and White Leghorns are Extended Black. The WL has Dominant White which is why the Tetra tints are white, but the Tetra Tint should be split for dominant white and one of the non-dominant white alleles. I think it is just non-dominant white. Since the Tetra Tint pullet’s father is a RIR, she has gold, not silver. I expect the Tetra would also be split for Mahogany and Columbia but I don’t think those are that important.
So a RIR rooster over a Tetra hen should give you about half red chicks. That’s where the Wheaton from the Tetra matches the Wheaton from the RIR. You should also get about 25% black and 25% white. That’s where the Extended Black in the Tetra is inherited. The black or white will depend on whether or not the chick inherited the Dominant or non-dominant white with the Extended Black.
There will probably be leakage and possibly some differences in patterns, but I think this will be the basic split. Half red, ¼ black, and ¼ white. Of course, I have very recently been wrong.