Secession is a risky business. Colonial concerns tend to not like letting go of their holdings, from which they often derive economic benefit. Wars for Independence are the natural result. Therefore, secessionist movements will often agitate fruitlessly for years and years. When the colonial concern itself becomes weakened, however, and it's ability to project force against the colony is thereby lessened, secessionism can suddenly become far more attractive as a serious political agenda.
This was a huge part of why the United States was able to break away from the British Empire, actually. A massive ocean and the Crown holding a ton of war debt already, plus tensions between the King and Parliament made conditions about as favorable as secessionists could hope for.
It's not simultaneous, per se, but if one colony grew bold enough to secede and drew the ire of the parent state... now that parent state is distracted/engaged and thus weaker. A second colony shaking off the yoke would thereby split the attention of the parent state, making both secessions more likely to succeed.
This iterates, and so rather than simultaneous, you have a nearly-simultaneous chain reaction as more and more colonies get in on the secession game while the getting's good. Pressure would rise to secede if any secessionist sentiment existed because after this wave finished, there would likely be a backlash making a second wave more difficult to launch. "Now or never" becomes the sentiment very quickly.
This is, by the way, exactly the nightmare scenario that Imperial powers are terrified of, and the main reason they tend to drop the hammer pretty hard on secessionists; if they don't make an example of the first, they embolden the n-th.
Being the first requires either political savvy to recognize that conditions are ripe and that others will follow suit if you stick your neck out there... or blind faith in the same. Being wrong has terrible consequences. Being right means glory and the esteem of future historians.
The first mover, therefore, either has been provoked in the extreme - or is distant enough from the parent state that they feel a measure of geographic safety from reprisal. Whether or not this is true is immaterial, it merely needs to be perceived to the point that someone's calculus favors the act.
EVE Online players and other internet communities have a name for this kind of chain-secession. It's known as a "Failscade."