It happens to both sides. Mostly because the queue system does not remove people from queues once they join one so when the 2nd one pops they do not enter it, then the queue system has to start looking for someone else to take their spot. If they would just make the queue system remove you from other queues when you join a match there would be a lot less of this and a lot less imbalanced scenarios.
Part of it is probably due to feds having things to do while waiting for matches so will finish up what they're doing, if they can, before hitting accept. As a Klingon you're just standing around doing nothing anyway so hit it as soon as it pops up, unless you're grinding repeatables.