It's very normal to have leaching water due to a rain, continue to leach after a number of hours, and perhaps a day. Depending on soil conditions, landscaping, foundation material, and the like, all these have an effect on how long water may leach. As you pointed out, the rain storm was a heavy one. If the ground becomes too saturated, the water has to run 'somewhere', hence, into your basement.
You may be able to alleviate this problem by inspecting your gutters, improving the landscaping, extending your downspouts, or adding gutters where there should be gutters. During the next rain storm, don your boots, your raincoat, and umbrella (all the while being mindful of lightening), and do a visual inspection. Watch how and where the water flows ALL around the house. Since water travels the path of least resistance, you may be surprised where the actual SOURCE of the excess water is being generated.