Can someone explain the interrupt procedure of an MCU when performing calculations inside it?
It is all very simple. If the stream of calculations depend entirely on the sequence of the A/D readings then YES the calculations must be completed within the allotted time slot between the availability of the A/D readings. 

With that said if there are characteristics of the computations that make some iterations take longer than others (especially  when that longer time overlaps the next A/D reading) then you will have to study and determine your long term average computation. Once you know that you can plan for these once in a while longer calculations by having the A/D interrupt do no calculations and instead put the A/D value into a circular buffer. The mainline code can take care of the calculations using values it pulls from the circular buffer. Using this technique things can still get done Okay. Keep in mind that stuffing things into and taking them out of the circular buffer does incur some performance hit.