As the titles says (this might be more clear though), weather abilities still have their effect on turns that other weather has been set.
Here's a short description of the start of a battle I had:
>Opponent sends out Pelipper, who has drizzle, causing rain, and Ludicolo (who likely has maximum speed investment), who has the ability Swift Swim
>I send out Whimsicott, who has Prankster, and Manectric (who has maximum speed investment)
>Turn 1, Whimsicott sets sunlight with Sunny Day, with priority thanks to Prankster
>Ludicolo moves next, despite not being Scarfed and the rain being replaced, and Manectric Mega Evolving

I've also tried this while replacing Manectric with a Chlorophyll Victreebel that had max speed investment, and despite what should be a speed boost due to sun, it moved after Ludicolo.

I haven't had the chance to try this out with other weather or other weather-based boosting abilities, but they also may have the same problem.

I've tested these two scenarios in Pokemon Showdown, and in both cases, Ludicolo doesn't move immediately after Whimsicott.

Not actually sure what to mark this, but its "technically" not a bug in a sense. Reforged is still implementing the speed battle changes for gen8. Which is basically what you're experiencing and being unable to replicate in Showdown.
Basically:

In Gen 8:
Speed is now recalculated in the middle of a battle. So in this case when your Whimsicott removes the rain, age recalculates speed of every pokemon and removes ludicolo's speed boost in rain.

However, In Gen 7 and b4,

Speed is calculated b4 the turn starts. So since rain was up, Game says your prankster goes first, then ludicolo(From Swift Swim), then the other pokes. So even though rain isn't present anymore, Ludicolo still gets the speed boost, because they didn't start recalculating speed in the middle of a turn until gen 8.