Tax implications are jurisdiction-specific and entity-form-specific: The tax rules in US differ from those in CA (e.g.), and (in US, for example) the optimal answer will differ depending on whether your biz is wrapped inside of an LLC, an S-corporation, a C-corporation, a general partnership, or a limited p-ship.
That's the fancy-pants way of saying that your best answer will come from your tax advisor who has all the details of your context in front of him/her, and who is a whiz at the applicable tax laws of your local, municipal, state/territory, and national domicile.
Very generally, though, first look to your partnership or shareholders' agreement. If well-drafted, it'll contain provisions for how to treat partner / co-owner advances and personally-incurred expenses. The agreement has the first and controlling say-so in the matter, if it has anything to say at all.
Absent that, you'll probably wanna modify that agreement ASAP to add such a section, in order to avoid misunderstandings and hard feelings. If you're sharing profits 50/40/10 yet one of the minority partners is building up a substantial additional investment in the biz in the form of business expenses on the ol' personal Visa, s/he might begin to feel the profit split should reflect that additional investment.
Alternatively, you could consider paying interest on these advances / loans, and retain the 50/40/10 split of residual profits remaining after taking the interest off the top. Depending on your structure and jurisdiction, there might even be a small advantage to doing so with respect to "self-employment" tax by converting a portion of what otherwise would have been income to a partner subject to SE tax, into non-SE-taxable interest income. Good idea here to (a) document the loan agreement terms with a written promissory note; and (b) make sure the terms and the interest rate are commercially reasonable for the context. That'll decrease the chances your applicable tax authority would deem the "loans" to just be equity in disguise, with potentially adverse tax consequences.
And generally, those deposits (cash advances by partners when the cigar box gets a bit low) should be booked either as loans (perhaps short-term advances) or additional equity, rather than "expense reports". Most times, the former is preferable over the latter, for simplicity reasons.
Best of success with the biz, and cheers!
...it was early and I was full of no coffee...