The only risks for HIV in adults are:
1) Having unprotected anal or vaginal sex, or
2) sharing intravenous needles with IV drug users.
There isn't any other situation that you can think of that would put you at risk for HIV. Your test only tells you about your HIV status, but if you have never done any of the activities I listed above, any test you take will be negative.
The other person's home test only matters if they take it at least 90 days after the last time they engaged in any of the risk activities listed above. If so, and it is negative, then there is no risk for HIV no matter what you do. Two HIV-negative people can't give each other HIV. If the test is taken before the 90 day window period, the person could still be HIV+.
However, if all you're doing is oral sex, none of this is a concern since it's not a risk for HIV.