You must follow all normal timing rules when casting a spell this way.

If the top card of your library changes while you're casting a spell, playing a land, activating an ability, or taking a special action, you can't look at the new top card until you finish doing so. This means that if you cast the top card of your library, you can't look at the next one until you're done paying for that spell.

Madame Web lets you look at the top card of your library whenever you want (with one restriction—see below), even if you don't have priority. This action doesn't use the stack. Knowing what that card is becomes part of the information you have access to, just like you can look at the cards in your hand.