A turn south would have flown us into the lead (easterly) jet, and you are assuming both F-15s don't change track. They were requested to stop climb as they approached the tanker (and reduced climb rate) so the geometry was against us in each case. A turn away increases the tanker's relative profile to assist visual acquisition and also was auctioned to take the aircraft away from the perceived constant bearing (visually) of the climbing fast jets. However, due to the lack of available response time, the tanker would have been in the same bit of sky whatever they did, once the decision to manoeuvre was made.
But I agree about the TCAS diminishing lookout. Not a factor in this case though since they were seen by me before the TA call.