Let's call your boat A (ahead), and the other boat B (behind) and analyze the situation in steps (which is how I like to walk through the rules during a protest hearing).

Step 1:
A is clear ahead and to leeward of B. B is obligated to keep clear of A under RRS 12 (on the same tack, not overlapped).

Step 2: A tacks. From the moment A passes head-to-wind, until she is on a close-hauled course, A is obligated to keep clear of B under RRS 13 (while tacking).

Step 3: A completes her tack. A is now on starbaord tack and B on port tack. B is obligated to keep clear of A under RRS 10 (on opposite tacks). A is obligated to initially give B room to keep clear under RRS 15 (acquiring right-of-way).

At all times, both A and B are required to avoid contact under RRS 14 (avoiding contact).

Now, if B has to take avoiding action during step 2, then A breaks rule 13. If B does not have enough time keep clear in a seamanlike way after A completes her tack (e.g., she crash-tacks or makes contact), then A breaks rule 15.

Note that B does not have to anticipate A's actions at any time. A may hail that she's tacking, but it's her actions that count. After A completes her tack, she must give B enough time to assess the situation, choose a course of action, and execute it in a seamanlike way.

It may seem counter-intuitive, but this is one of those situations where the give-way boat contols the right-of-way boat's action. Given the situation you were in, you did the right thing under the rules and let the F18 drive you past the layline.

As Rick pointed out, this is a tactical situation you want to anticipate and avoid. Some of the options you could have employed earlier are:
1) pinch up in front of the astern boat, so you are able to tack when you want,
2) foot away, so there is enough space between boats for the other to keep clear after you tack,
3) come in to the mark on the port-tack layline and scrape the astern boat off around the mark.

Of course, there are potential difficulties with each option. If you pinch up, the astern boat is likely to pinch up as well. If you foot off, the astern boat may foot too. If you approach the windward mark on the port layline, you may run afoul of other boats rounding the mark.

Regards,
Eric