I am in Oklahoma and Missouri typically gets what we get, just hours later.
Yes, May is the month for tornadoes and violent storms. You will have a 25% chance of "rain" on any given day in May I would guess. However, "rain" typically lasts only for 30 minutes or so. So while the forecast calls for a 90% chance of rain, you may not even get wet if you see it coming on the radar and duck into a cafe for that second breakfast or afternoon ice cream while it passes.
As far as the storms go, yes, they can be quite exciting if you are actually in one. For instance, I have seen quite a few tornadoes from as close as 1/4 mile away and all is well. If you are directly hit by one, then that is another story. That said, if you follow the locals' lead, you will be fine. If the locals are going about their business when the sirens are going off, do not worry, seriously. Sirens are to give a warning that there is a possibility (or an actual one if spotted) of a tornado in the "area" (up to 30 miles away). The locals keep well aware of what is going on and a tornado may be 10 miles away but it is headed away from you so all is well (at least for you). The forecasters here are actually pretty good and if a tornado actually touches down, there are enough spotters around they know within a 1/2 mile of where it is. Listen to local radio and know the county and area you are in if things look bad.
Honestly, the best thing to do is shelter in a restaurant, library, hotel, etc. if the weather radar shows red or darker storms. Wait until it passes then carry on your way. Red storms have very strong rain. Yellow and green is rain but not much else.
Another really good thing to remember is be aware of hail. If during the daytime the sky is "green", you should really seek shelter as there is a massive hail storm nearby.
Don't let any of this scare you, just be aware of your surroundings. As a side note, a regional group of bike tourists are planning on touring in Missouri for about 4-7 days this upcoming mid to late May along parts of the Katy and Rock Island trails and we are more concerned about how "slow" the Katy and Rock Island gravel surface gets when wet. The tornadoes do not even factor in to our decision where to ride.
Tailwinds, John