J had it right. "Top of the tide" is just another way of saying high tide. There is no "bottom of the top" (or "top of the bottom" for that matter). If the fellow you were conversing with seemed to be referring to an extended period of time, it's possible he used "top of the tide" to mean the hours of highest water during the tide cycle (i.e. 3 hours before until three hours after hight tide).
I understand your confusion though. Some people use the terms "up tide" and "down tide." Some use "up tide" to mean high tide, others mean it as rising tide. So trying to decipher a statement like "I took the fish just short of the up tide" can be a chore. There are other people who will say "flood tide" to mean high tide although really this is inaccurate. A flood tide is a particularly high high tide caused by the new / full moon or less often a big storm. Lunar tides, solar tides, spring tides, neap tides, perigean tides, apogean tides, gravitational tides, centrifugal tides ..........I'm actually working on an article right now that attempts to sift through all this. My head hurts.
PS: When your wife says "bottom of the Tide" it usually means you're out of laundry detergent.
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