Who actually cuts my half of the JV fee, title or my partner?

Both happen, and the difference comes down to what paperwork the closing agent has in their file.

Quick definitions first. The assignment fee is what the end buyer pays you to take over your purchase contract. The JV agreement is the separate one-page-ish contract between you and your partner that says who does what and how the fee splits. The settlement statement is the closing agent's line-by-line record of every dollar in and out.

A title company or closing attorney disburses to the parties their documents tell them to pay. If the assignment names only your partner's entity, the fee lands with your partner and your $5,000 depends on him honoring your side agreement. If you send the signed JV agreement to the closing agent well before closing and ask them to disburse per its terms, many will show two lines and wire both of you directly. Some won't, because escrow disbursement practice and what a closer is willing to do vary by state and by company, so ask the specific closer in writing before you're relying on it.

The part that catches people is the earnest money and the marketing spend. If you paid a $500 deposit and $300 in mailers and the JV agreement doesn't say those come off the top before the split, you're eating them out of your half. Write reimbursement into the agreement.

Also, whoever receives the fee usually gets the tax paperwork for it, and how that flows to you is a question for your own tax professional.