Assuming Varys had Tyrek Lannister abducted during the riot, how would he have gone about planning it? Did he just suspect there would be trouble and have his catspaws tailing the procession, read to move if the opportunity presented itself? Do you think he also tried to have Sansa abducted at the same time?

Varys was completely aware of rising tensions in the street and it wouldn’t have been hard for him to escalate a situation by seeding a crowd with little birds with rocks to throw. But given that a riot was pretty much inevitable, I think he focused on planning on how to get his hands on a Lannister without leaving a trace. 

And no, I think if he wanted Sansa abducted, we would have seen signs of that, more akin to Ser Shadrich.