Yes the caul is necessary and exactly for the reason you anticipated to spread things out. It need only be a very simple shape that fits between the X-brace and has a modified side for the first tone bar. StewMac used to sell one that was made out of material that glue does not stick to. I've used this one hundreds of times and I don't have to cover it with waxed paper (so the glue does not stick).
We set-up our clamps to hold the caul in place when using HHG and time is limited. You can used Titebond original if you are not tooled-up and knowledgable about HHG it's unforgiving in terms of open time and bridges are one of the most difficult things to glue because of the time required to get the clamps in place. I don't recommend HHG unless someone is comfortable and knowledgeable about it's use.
Frank Ford RIP once posted on this forum that he finds the biggest clamp he can find and clamps the hell out of the bridge. Now after reading this you tell me if this caul is necessary...
It is you do not want to crack the bridge plate and I will remind you and everyone else that a bridge plate has six or twelve holes in it all in a line making it just asking for the perfect uneven pressure to crack the sucker along the pin holes....You can tape with masking tape the caul in place and then when the clamps are in position they will hold it. Be sure to remove it when done too
* Just checked StewMac they no longer sell the non-stick caul and I'm home so I can't take a pic of mine that is in our shop in Ann Arbor. What I like the most about my caul besides it's non stick for Titebond and HHG is it's about 1/2" thick, made of cutting board like material and can slightly flex.
Your guitar has a slight dome on the top and I like a clamping caul to not be rigidly flat but able to slightly conform to the curve and dome of the top. The caul I speak of can do that. If you have an old cutting board of non-stick material it would be perfect to cut up.
But you can make one of our plywood or just plain wood just cover it in waxed paper so it becomes non-stick too. It should cover the entire bridge plate.
The height of the caul is also necessary to clear the X-brace intersection with the clamps. Not all C-type-clamps have an adjustable lower contact point and need to clear the X-intersection.
The bridge patch top side should be expanded and cleared of finish very close to the bridge perimeter. The bridge patch needs to be cleaned up of all old glue and finish and so too does the bridge bottom. I scrape my bridge bottoms to conform to the top with only minimal finger pressure required so the bridge is sitting all the way down everywhere especially the wings.
You may need two or three clamps too to get it to sit down everywhere and this is normal although again a well fit bridge can be done with one clamp with a topside caul with adjustable wing hold downs.
If using Titebond original or HHG wait 24 hours before putting strings on. Keep clamps in place at least 4 hours I usually leave them for 12 - 24 hours.
You can make a two layer masking tape well around three sides of the bridge making positioning it for gluing a snap AND it removes with the removal of the tape 5 minutes after the clamps are set it removes 3/4 of the squeeze out in one easy operation.
Bridge reglues are not overly difficult but they are unforgiving in positioning things, clamping and glue open time. Because of string tension this is one of the most critical glue joints on the instrument.
Lastly so why did it happen? This is the time of year when acoustic guitars that are not humidified shed bridges. If a dry guitar is the culprit I would remedy that before I reglued the bridge so that the top is not a moving target for the new bridge glue joint.
But to your original question is the caul necessary - yes.
