The answer to the same question I posted on Movies.SE
The creators of the show have already said that the timelines of different places is not in sync. Some places move forward in hours, some in days and some in months.
Writer Bryan Cogman, who wrote episodes 6 & 7 of season 6 had this to say
The timelines between the various storylines don’t necessarily line up within a given episode. For instance, the ‘Northern Tour’ Jon and Sansa embark on would probably take a couple weeks, but Arya’s storyline over the past few episodes only spans a few days. We realized a while ago that if we tied ourselves in knots trying to make all the ‘story days’ line up between all the characters the momentum would suffer.
Varys leaves Mereen in episode 8. He is seen in Dorne in episode 10. So, that's believable. He gathers the support of Dorne and Tyrell ships and goes back in the same episode to Mereen. Varys doesn't have teleportation power because you can see Tyrell and Dorne ships along with Greyjoy and Targaryian ships in the naval fleet of Dany. You can't teleport ships so it is to be assumed that Varys sent a word back to Tyrion telling him that Tyrell and Martels are behind Dany now, so wait up. Varys must have got back with a token ship of Tyrell and Martel each with some envoys to prove their support.
Screenshots of Martells & Tyrells ships with sunspear & rose as the banner:
House Tyrell ships - So Timewise we can assume Varys Travelled to Dorne and back with the Martell and Tyrell fleet.
Tyrell sails, Martell Sails, and Targayen Sails - How Varys Returned to Slavers/ Dragons Bay