Warning: Sarcasm ahead...and then my opinion.
Looks like you'll be fine so long as it never rains harder/more than it just did. In other words, it's going to be a problem at some point. I'd ignore anyone who says otherwise until you find a contractor who gets it and knows what they are doing. But the time to find them is before the first storm much bigger than the last storm.
That said, if it overflows into the pool before it gets fixed, your pool won't cease to exist, it will just need a serious intervention (a few days to a week or more of effort to clear the water). If you don't get it done and the season ends, you have another 9 months or whatever to resolve the potential issue. When deciding if you believe the folks who've told you "it'll be fine", think about if you would be comfortable going on vacation during the monsoon season as is.