Put. on your poncho, and continue. We always carry a cheapie (less than $1) poncho in our back pockets when we go to Disney. When it rains, we pull it out, put it on and go. At this point, we're all very good at getting inside a covered area, taking the drippy things off, shaking off the excess water and folding the ponchos back up small enough to go back in the pocket. We re-use the same cheap poncho several times before they get ripped. I usually take one per person for every 2-3 days we're going to be there...so for a week, I'd take 3 per person.
You can find the cheapie ponchos at Walmart, in the Camping department...last time I bought them, it was was like 89 cents each.
IF you're there during hurricane season (June-November) then you may want to get the more expensive heavier gauge vinyl ponchos (like the ones they sell in the park...you can get that type at Walmart also for $6 or $7) REason for the heavier ones is the storms during hurricane season tend to have strong winds that will rip the cheap ponchos to shreds quickly.
But for the usual cloud-burst at Disney during this time of year, the cheap ones will do fine. AND another tip..if you're at one of the night time spectaculars, like Fantasmic or Illuminations, and it gets way too cold to be comfortable...put on the cheapie poncho...it will insulate you and you'll soon be toasty warm. In the winter, even when it's sunny and warm during the day, the night time temps can drop off quickly.
As for tips...well it used to be that most people would leave when it starts raining, but our experience of numerous trips during the last 5 years is that most people do not leave unless it's pouring rain for hours and hours and hours. IF it's light rain, most people stay...or even heavy rain that's over quickly, they stay. So the lines may get a tiny bit shorter, but not a lot shorter, not any more. Mainly the only people we see leave when it's raining are those with babies in strollers...everyone else just trudges on to the next attraction. After all, the majority of attractions are inside...but even the ones outside still run in the rain as long as there is no high winds or lightening close. The only consolation if you get an all-day downpour is that the ride lines DO go down dramatically if it continues to pour all day. The puddles are deep...and the pavement gets slippery, though, so watch where you walk and don't let the kids run ahead (we've seen some pretty bad falls from slipping on slick pavement at Epcot.) We have been there when the walkways are over-the-ankles flooded...that's when there's no line at all at Soarin' in the middle of the day.