To add to Salvo34's good info.
You ask why (how) does Premiere pro 'work' with 24fps in a 60fps timeline ...
PP repeats frames. In each (60 frame) second it's repeating each 24fps frame at least twice and a few three times. How it repeats these frames is determined by your choice of 'time interpolation'. By default this is set to 'Frame Sampling'. Basically repeating frames to add up to a total of 60fps.
You can make a different choice - right click a 24fps clip in your 60fps timeline and select 'Speed/Duration' from the pop-up menu.
Then under 'Time Interpolation' you can choose from the default or 'Frame Blending' or 'Optical Flow'.
Optical flow will create new frames by analysing the clip and actually tracking pixels to create a 'real'
60fps clip from your 24fps source. This is not wothout issues (+rendering time) and sometimes you will see weird artifacting when the analysis can't perfectly figure out where pixels are moving.
The downside of this is you will lose that '24fps look' that you like. Stay with Frame Sampling - or try 'Frame Blending'.
Frame blending will help hide any frame judder that you might get from just Frame Sampling.
Mixing frame rates is very common (for me). I'm mostly working at 25fps - TV over here is 25fps (50i) so most everything is shot 25 (or 50i). But I'm constantly using stock footage at 24 and 30fps and footage from countries that use 29.97. Where possible and mostly with 24fps footage I do something different - use > Modify > Interpret Footage and change 24fps footage to 25fps. Not something you want to do as your 'use case' is different.
Putting an interview shot (your speaking segments) that were shot at 24fps into a 60fps timeline AND leaving at the default setting usually looks just fine in a 60fps sequence because there is usually not much movement with this type of footage. It's movement that will show up some problems. If you look carefully - say when someone moves their arm - you might notice the repeated frames. i.e. the movement might look like it has some hesitations. This would be where Premiere Pro has repeated a frame 3 times - so the movement has this (almost imperceptible hesitation) due to that extra repeated frame. If this is not noticiable or does not bother you - don't worry about it.
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