RI has a republican governor due to Almon having high approvals at the time, and Carcieri just came in at the right time. Just like Mitt Romney came in due to Cellelucci high approvals at the time. Approvals of governors matter as well.
This is not accurate. Almond's approval ratings were in the 20s by the time he left office. In fact, they were in the 30s even around the time he won reelection in 1998.
The reason Almond won in '94 and '98 and Carcieri won in '02 were because people did not like their opponent: Democrat Myrth York. Despite being a Democrat, she just never clicked with voters and lost by a larger margin each time she ran.
In contrast, since the station nightclub fire of 2003, Carcieri has been decently popular and this allowed him to just barely win re-election against a stronger opponent.