which order to file of 2 state part-time resident

No, the states do not send money to each other.  

Which state is his resident state or did he live in each state for part of the year?

If he lived in each state for part of the year, then he would file 2 part year resident returns allocating the income so that only the income that he earned while a resident of that state would be taxed by that state.  This would avoid him being taxed on the same income by each state. 

If he was a resident of one of the states and just temporarily left to work in the other state, then he would file the non resident state first and then on the resident state, he would claim a credit for the taxes paid to the non resident state.  

Multiple States

File Non Resident State Return