Alright, so this isn't so much a rules question as it is a rules discussion. While driving home today, I was idly thinking of the finer points of pairing a Tractor Beam with Ruthlessness, and I was trying to figure out if it's legal and possible for the controlling player to choose whether or not to trigger the splash damage before and/or after the movement, or if it must be only one or the other. I mean, it would be great if you had the flexibility. But in order to figure this out, there are some finer minutia to dig into. So let's start with the basics.
When a player controls two effects that both trigger at the same time, that player decides which effect occurs first. Okay, easy enough to deal with. After all, when I have two or more ships with the same PS, I get to pick who moves or fires first. So let's take a look at the exact text on Ruthlessness:

"After you perform an attack that hits." Which means Ruthlessness resolves after the entire attack has been decided. We're good so far. So let's say you perform your tractor beam (which is of course a secondary weapon attack, which qualifies for Ruthlessness). Exactly what happens then? Well, let's say the attack will hit. Here's where the fun begins.

"If this attack hits, the defender receives 1 tractor beam token." Hmm. Okay, interesting. But then it says "cancel all dice results". So if I'm not mistaken, the token is assigned not after entirely resolving and performing the attack, but actually within the individual steps of performing an attack. More specifically, the token seems to be assigned inside the "compare dice" step, since dice are cancelled in that step and cancelling dice is the very last line of text on the card.
So if I'm reading this correctly, the token is assigned before the attack is actually fully completed. Though not found on the upgrade card itself, the rules insert for Tractor Beam tokens reads in part:
"The first time a small ship receives a tractor beam token each round, the opposing player chooses one of the following effects:
- Perform a barrel roll using the [1 straight] maneuver template. The opposing player selects the direction of the barrel roll and the final position of the ship.
-Perform a boost using the [1 straight] maneuver template."
Taken at face value this seems to imply that the movement occurs immediately upon receiving the token. And we've already established that receipt of that token occurs within the "perform attack" part. So, based on what I've gone over here, I'm lead to believe that no, you don't get to decide whether to apply the damage from Ruthlessness before the movement forced by Tractor Beam, only after resolving its new position does it apply (and as such, this is the ruling I'll be going with until further notice).
However, I could be wrong. There is one thing that I can't remember... exactly. I feel like I can recall a rule about timing and resolution that states that effects from one card can't interrupt the resolution of another. If that were true, Tractor Beam would assign its token, at which point the Rules Insert and Ruthlessness would occupy the same moment in the Resolution queue, putting them both firmly in the "player decides the order" category. If anyone knows more about this, please make it known.