Water dripping under vinyl siding onto basement concrete
Any leakage is a problem. It can get worse through building movement or freeze/thaw cycles. It can lead to other problems like mold. 

So moisture is either coming up from below (a rising water table) or its coming from the surrounding ground water in the saturated soil.

If it comes up from a rising water table, it will enter the living space from below through the crack between the foundation wall and slab.

If it comes from the surrounding ground water, it COULD enter the living space through the wall, especially if the exterior side of the foundation wall is not sealed properly.
Either way the moisture enters the living space it will need to be collected and disposed. I think the best way to collect it is on the exterior side of the foundation wall in drainrock and a perf pipe laid 6”-8” below the interior basement slab.

To keep the subsurface water from seeping through the wall, I recommend installing a moisture barrier on the exterior side of the foundation wall and install a 2” thick plastic mesh on the wall to allow water to flow down to the perfect pipe. If dirt is allowed to be backfilled against the wall, the dirt could hold the moisture giving it a chance to seep through the wall.

Once collected it needs to be disposed by extending a solid pipe over an embankment or in a collection well and pumped away.

This is expensive so you may want to monitor it for a season or two. This may be the most expensive method of solving the problem, but it’s sure to work.