Ag-Sn-Cu Phase diagram to formulate homogenization temperature / duration
Much of this answer is based on a document available from NIST at Properties of Ternary Copper-Silver Systems [originally J. Phys. Chem. Ref. Data, 6(3) 621-673 (1977)] - this has an equivalent to the diagram in the question (which is just the surface of the liquidus). Now, since you are talking about balances of solid phases, it is also worth looking at the binary diagrams to discuss those.

For Ag-Sn, one gets:


For Cu-Sn there is:


Now I'll throw out a few observations:
Ag$_{3}$Sn is a line compound, which in the binary system is not stable above 480C. In the NIST report this phase is referenced as $\theta$, but called Ag$_{3}$Sn($\epsilon$), causing great confusion since the $\zeta$ Ag-Sn phase is designated $\epsilon_{2}$, and Cu$_{3}$Sn($\epsilon$) is designated $\epsilon_{1}$. So, watch it...

The Cu$_{3}$Sn line compound converts to the fcc $\gamma$ phase at around 676C. The $\gamma$ phase is sometimes also referred to as Cu$_{3}$Sn (yet more confusion possible). The Cu$_{3}$Sn and Ag$_{3}$Sn line compounds are different crystal structures, and do not form a solid solution across the ternary.  

For both Ag-Sn and Cu-Sn, another thing to notice is the various other phases that are in close proximity to the Ag$_{3}$Sn and Cu$_{3}$Sn line compounds. Going into the ternary system, you get questions like how adding Cu into $\zeta$Ag-Sn impacts the free energy. 

So, what now? In the NIST report, on page 664 is a pseudo-binary diagram where the Sn wt% is held at 20%, and Cu wt% is varied from 0 to 80 (balance Ag). Personally I hate weight percent, but...  The point that one can eventually pick out is that the Ag$_{3}$Sn phase, designated $\theta$ appears almost nowhere - there is just a little sliver way over near 0 wt% Cu and under 250C. It appears that with the addition of Cu, the $\zeta$Ag-Sn phase rapidly replaces the Ag$_{3}$Sn phase.

So, as far as I can tell, I'm not sure that the kinetics even matter here. You basically can't get much Ag$_{3}$Sn to form within the ternary parameters you have chosen - you will get $\zeta$Ag-Sn instead.