OK, here's that diagram again:
And the question: Do you need
complete isolation? Probably not.
However, what isolation is concerned with, is segregating the currents that drive the relays, from the power supply to the Arduino. So you can use your buck converter module to power both. Note the diagram: You must have one
pair of wires running from the output terminals of the buck converter to Gnd and JD-VCC on the relay module. When I say "pair", I mean the wires run
together.
You now have a second
pair of wires running from the same
output terminals of the buck converter to Gnd and Vin/ "Raw" of your 3.3 V Arduino. That wire from VCC on the relay module travels
together with the "IN" wires from the relay module back to the Arduino Vin pin. This means that you have a quite separate circuit from each part back to the output capacitor on the buck converter, minimising the tendency of impulse currents from one (actually, the relays) to affect the other.
So why a 3.3 V Arduino Pro Mini? Pro Mini itself is perfect, but 3.3 V an odd choice. You are clearly not saving power!
Note of course, that the 3.3 V Pro Mini outputs switch between 0 and 3.3 V, while the relay module VCC comes from 5 V. This is absolutely correct - the relay module has two LEDs in series on its input with a combined voltage drop of 2.6 V or so, so it may not reliably switch from 3.3 V alone and will certainly
not conduct at the difference between the 3.3 V HIGH and 5 V, but when the outputs go LOW it will see the full 5 V and operate reliably.
OK, to help you follow this, here is the circuit of the relay board: