The concept of "phases" is quite deliberately not included in Minion. Initiative is provided so that you can apply initiative within the specific phases relevant to your rolemaster version.
So in your case, assuming you're using RM2 rules, simply scroll through the entire initiative sequence for the Spell Phase, resolving any character that casts spells, then for the next phase - Fire phase - continue clicking the initiative so that it starts again from the 1st Actor and sequence through to resolve any characters that Fire missile weapons, etc. For RM2, you would probably scroll through the initiative sequence 4 or 5 times, for the 4 or 5 phases.
If playing RM Classic, you would scroll through the initiative sequence twice, for the two phases. For RMSS/FRP it's different again.
Note that you should not think of Minion as a "Rules Engine". Minion enforces no rolemaster rules. It is you, the GM, who enforces the rules from the version of rolemaster you are playing. Minion is simply a tool that simplifies many of the menial chores required during a combat encounter.
Hope that helps. Cheers.