When your forward flight exceeds a certain speed, as you noticed the flight characteristics of a heli start to act very similar to a fixed wing plane. The rotor disk acts like a fixed wing and the tail rotor acts like a fixed tail, even in real heli's. In fact, there is a guy that makes small model heli's that don't even have a tail rotor, just a flat disk. Of course they can't hover but he just tosses them and goes straight into forward flight and they fly fine.

The gyro complicates matters a little bit because it's job is to reduce yaw, so you may need some rudder input to let the gyro know that yes, in fact you are turning and would like some yaw in there A rate mode gyro (which the Blade CP+ comes with stock) will allow the tail to come around a bit on it's own without a lot of rudder input (depending on the gain setting). It limits the rate of yaw, but doesn't hold a specific heading so the tail will come around as you turn (or even "weather vane" nose into the wind when hovering).

If you upgrade to a heading hold gyro, then rudder input is essential to make a coordinated turn since the gyro will want keep the nose pointed in the same direction (holding the heading just like the name says) regardless of which direction the heli is actually moving (flight path). If you bank to the right without rudder, the heli will "slide" to the right while still pointing in the same direction (like a plane would if you banked right with left rudder)

Most (if not all) HH gyros can also be switched to rate mode since rate mode may actually be preferred for forward flight due to less rudder input being needed.