The tides are part of a balancing system
If your flying island is actually continent-sized, the moon's gravity would affect parts of it at different times, causing it to rock or sway just a little, but enough to put serious stresses on the internal structure, reducing its lifetime.
Whether by design or natural selection (all the other continents crashed long ago), your continent has long underground water channels running in the direction of the moon's orbit. The water moves back and forth with the moons, balancing the moon's upward pull with extra mass and keeping the continent still. Some or all seas are in contact with the channels, giving them tides much stronger than their own size would suggest.
Alternatively, the water is moved around by magic. Nobody knows how, but smart people theorize it keeps the continent from tipping over somehow. This scenario would not even need a moon or predictable tides. Seas could experience ebb and flood at seemingly random times and ranges.
(old answer below, invalidated since the continent floats in the air, not on the water).
The inland sea is connected to the ocean (underground)
You say that your continent is floating and for this answer I'll assume it's on the ocean, not on the rocky mantle deep under any ocean.
To have high tides, you need a large mass of water (larger than just a lake or sea) and a favorable coastline that compresses the water flow in the direction of the tidal flow. On Earth, those happen mostly around Alaska and Canada as explained here, while in the southern hemisphere, there is no similar effect.
Your continent is probably looks something like a giant island (say Australia) on a map and is surrounded by open ocean, so it might not experience very large tides on its outside coast, but it still gets them. While there is no narrowing coastline, there is still a compressing of the flow happening as it goes under your continent, increasing the pressure.
If your inland seas are connected to the ocean through holes in the bottom of the continent, there might be water flowing in and out with the tides, causing the sea to have ebb and flood, although it will happen nearly simultaneously around its coast.
Of course, this would probably be accompanied by extreme currents and a maelstrom here and there, depending on how deep they are. If that is not the environment you want you seas to have, you could instead make the thin bottom of the sea somewhat flexible, to the point that the entire sea bottom rises and sinks a meter or two from the pressure changes in the ocean under it. Whatever material or magic (or turtle) is holding your continent together (and floating) can include the flexible aspect.