I have no problem with Hurt, Tennant and Smith's Doctors realizing they needed more computational power to create a planetary-wide stasis field. So they went back and convinced past doctors to do the computation and to show up.
I know some are worried about past doctors knowing the future and the consequences of it. But I feel it shouldn't be too hard for the 3 doctors to convince the past 8 doctors that what they are doing is absolutely critical to Gallifrey's survival and to do it with the TARDIS on autopilot and sensors completely turned off so they don't know exactly what's happening or when it happened.
Capaldi's doctor shows up because he already knows he's needed.