Tomorrow replaces each of your draws with something that is not a draw (despite the fact that it puts the card in your hand, it does so without using the 'draw' keyword action), so you never technically drew a first card, so Spirit of the Labyrinth never cares. You will be able to replace what would be multiple draws by Tomorrow's effect.
Tomorrow's effect is mandatory and is in place for every draw action as long as it's on the battlefield, so that usually won't come up with it, but note that if a player actually draws a card during a turn, he cannot replace further draws with a replacement effect (like, say, the dredge ability). The draw action cannot be attempted at all, so it can't be replaced.
I'm a former judge (lapsed), who keeps up to date on rules and policy. Keep in mind that judges' answers aren't necessarily more valid than those of people who aren't judges; what matters is we can quote the rules to back up our answers. When in doubt, ask for such quotes.
Thank you!
Tomorrow's effect is mandatory and is in place for every draw action as long as it's on the battlefield, so that usually won't come up with it, but note that if a player actually draws a card during a turn, he cannot replace further draws with a replacement effect (like, say, the dredge ability). The draw action cannot be attempted at all, so it can't be replaced.