This is a good question!
You're right that llevo is the present tense and not the future here; however, it isn't incorrect in this situation. This is because tenses aren't as simple across languages as one might think. In Spanish (and in other languages), it is sometimes possible to use the present tense to talk about things that would be in the future tense in English. This usually happens in colloquial conversations.
For example, a native Spanish speaker might volunteer to do something for someone by saying Yo lo hago. This literally translates to "I do it." In English, however, one would normally say "I'll do it" in this sort of situation.
This is the sort of colloquial construction that you'll get more used to as you spend more time with the language, and as you interact more with native speakers.
I hope that this was helpful!