First let me say that I have only experienced this "phenomenon" with a fleet of 20 hp Hondas with trim tilt and have never worked on a 90. But, what you describe is exactly what I experienced with a customer that refused to keep their fuel tanks out of the rain.
These engines (20 hp) have a black, rubbery thing attached to the engine oil dipstick tube. It looks like some sort of large, inline, fuel filter. Honda calls it a "fuel resevoir". I think they put it there as a water separator. I can tell you it works great as a water separator because that's what I find in there with water contaminated fuel. If you have one of these contraptions, take it off and shake all the liquid out before trying to start your motor again.
What is happening (in my opinion) is that you have gotten water in your fuel and it has pooled in your float chamber bowls. The carb picks up fuel from the bottom of the bowl but if there is water there, you are feeding it water and no start. When you tilt the motor, as you say, and it starts, it's because you are sloshing the gas that is floating on top of the water, over and giving the carbureator a brief "gulp" of fuel. You need to check your tank for water contamination and drain the carbs and all lines including the fuel resevoir that I described.
Sadly, Honda carbs do not do well after ingesting water and it is also my experience that you will still very likely have runability issues until they have been thoroughly cleaned. But, you may have caught it early and a good fuel system flush and a dose of Sea Foam in the tank may be all that you need.
To verify water in the tank, I use a fuel line assembly with a primer bulb but with no fuel connector on the outlet. Since any water in your tank will pool at the bottom, water will be the first thing the in tank "dip tube" will pick up. The tank needs to sit undisturbed for a few minutes for the fuel to settle. If you pump several millileters into a glass jar and let it set only a few seconds, you will see the water and fuel separate. This isn't the only way to do it but it is my way and always yields results that I can show my clients. I feel like Merlin the Magician each time I hear the "audience" gasp when they observe the water that they have been unknowingly carrying around.
If you find water, you then need to find out where it came from. Sometimes it can be as simple as humid air condensing moisture into the tank. Or, it can be like my group leaving their tanks out in rainstorms with the vents open. If you suspect that the place you purchase fuel from is where you get it then you kinow what to do.
Good luck