How are tandem breakers used in multi-branch circuits?
By "multi branch circuits" you mean multi-wire branch circuits or MWBCs.  

How do MWBCs and tandems go together?  THEY DON'T.  

Either 


the electrician ran new wire, eliminating the MWBCs,  or 
he carefully placed them on opposite poles (you have to know how to do that) and totally ignored the Code requiring handle ties, and is just hoping the next guy doesn't carelessly rearrange them onto the same pole, or 
he slapped them on a tandem and the neutral wire is glowing cherry red right now. 


If you want to do that same thing, your best bet is to put both pairs of your MWBCs onto a 2-pole/2-pole quadplex.  That's what he should have done.  

Making your own handle tie is out of the question.  Listed handle ties arent available for duplex breakers, but they don't need to be, since quadplex breakers are readily available.