This valve comes through the house's insulation and wall. Heated side left, outside right.
Those aren't residential outdoor faucets. Those are sillcocks.
You've linked a bunch of hydrants/sillcocks, which put the valve proper inside the building, and the handle and spigot outside the building. The purpose of those is freeze protection in winters.
The trick is to drain the water in the 6-30" of pipe coming through the wall. That won't happen naturally. Vacuum, combined with surface tension across the small spigot outlet, will hold the water in there. So these hydrants have a "vacuum breaker" which allows passage of air in, but not allow water to gush out. The water drains out the normal spigot.
Which means, if something is blocking the spigot, it will fail to drain.
The thing blocking it could be an extension hose (it doesn't even need a valve at the far end; a long enough hose will do), or a hose reel, manifold, timer, you name it. Any of these will defeat the sillcock's self-drain ability, and result in freeze damage to the sillcock.
Further, if something like that has a valve of its own (think manifolds), it will entrap water pressure between the accessory's valve and the hydrant's valve. The vacuum breaker isn't made to have pressure on it 24x7, and may stick or rust closed, which is what the warnings are telling you.
So, basic sillcock hygiene 101, unhook everything attached to it at the end of the day.
Dump the sillcock. You need a plain faucet.
The valves you want to use are made to use with a plain faucet, or are made to be hard-plumbed. So get one.
You'll have freeze problems in the winter of course, so install that line in a way that lets you drain it. I like to place a shutoff valve then carefully slope the pipe to (or away from) a faucet I add indoors, so I can close the shutoff, then open that faucet and the outdoor ones, creating a "vacuum break" so gravity will drain the water. Obviously if the low point is indoors, you'll need a bucket or put a hose on it (which is why I use a faucet :)
Or perhaps a more "pro" solution would be better
Another option is to (indoors) plumb in an industrial-quality solenoid valve. Have that supply your irrigation lines. The solenoid valve would open the water line when you apply something like 24 volts AC. Where would that come from? A plug-in wall-wart transformer. Now this changes it from "needing a water timer" to "needing a lamp timer". Now you can use any lamp timer, X10, any of a variety of smart controllers for plug-in lamps, etc.
The exit of the building could be a sillcock, since the control valve is indoors and comes before the sillcock, hence pressure would be removed when the system isn't irrigating. However with the hoses permanently attached, it would be on you to disassemble the system before the first freeze.