Nick here from Shopify. Really good question, taxes can be difficult, even on the best of days!
The first thing I would suggest is to reach out to a local tax expert or accountant to ask them as they would know best. We can't give tax advice on what to charge per se. Are you based in the USA with the influencers being based in the EU? If you ship someone something and it's not an order, then I don't believe you would need to pay a tax, but if you ship via your store for inventory purposes, it might be best to check with a tax professional to be 100% sure.
Hope this helps!