First a little vocabulary clarification so that we can be sure we're on the same page. "AutoFill" does not exist in filemaker. You can define a lookup to physically copy data from one related table to another, you can define calculation fields and auto-enter by calculation fields that combine and copy data from a related table or tables. You can also simply place the field from the related table on your layout--I think this is what you should be doing here.
What is the relationship linking your two tables? Is it:
Table 1::SiteName = Table 2::SiteName ?
If so, just place the State field from table 1 on your layout that displays records from Table 2. If the two SiteName fields match, you'll see the corresponding state name from Table 1 on your layout.