So how the deposit works depends on if you mark the deposit on the invoice or the job/quote.
In most cases, people are taking the deposit on the job after winning the quote. In that case, Jobber will prompt you to add that deposit to the billing history, and this is done before the invoice is created at the start of the job. Thats the most common workflow since that way the deposit will be transferred from the job, to the invoice when you go to create the invoice.
If you add the deposit to the invoice, then it is not added to the billing history automatically since you only added it to the invoice and not the job. That is something that I will mention to the devs though. The invoice that you send will still be correct, but an invoice is generally something that is pending, so once the invoice is paid, then it is recorded in the billing history and so will that deposit. You can also go and manually add that deposit to the billing history, but that might have to be done in the tablet view and not the mobile view.
So in essence, enter the deposit first, before you do the invoice, and the deposit will show up in the billing history and be carried over to the invoice when you go to create the invoice.
Let me know if that does not make sense.