You've pointed at what seems to be a continuity error, but I think you're reading Thor's statement too literally.
In the movie Avengers, Thor says that the Earth is ready for a higher form of war (because S.H.I.E.L.D. were using the Tesseract to make energy weapons)
Surely, the cosmic beings would be aware when the Red Skull was using the Tesseract if they are aware when S.H.I.E.L.D. does?
The actual quote:
Your work with the Tesseract is what drew Loki to it, and his allies. It is the signal to all the realms that the earth is ready for a higher form of war.
You're assuming that using the Tesseract makes the cosmic beings come to Earth. In other words, you're assuming that it is an actual signal, i.e. a broadcast or a homing beacon.
But I read Thor's quote much more figuratively. It would've been better for him to say "sign" instead of "signal", because that avoids the ambiguity that you're getting caught up on.
Avoiding the ambiguity, Thor's intended meaning is closer to:
As humans will now be wielding more powerful weaponry, they will draw the attention of more powerful opponents. Don't think that you're now the strongest of the bunch because you now have better weapons.
Thor wasn't speaking about having used the Tesseract, but about the impending upgrades to human warfare abilities. The energy weapons had proven to be an efficient weapon, why would humans suddenly decide to stop using energy weapons?
On more than one occasion, Thor has spoken words of wisdom, which are clearly based on Asgardian history (as the Asgardians are ahead of us). Thor's historical knowledge can be considered a warning for the future of humanity (as we have yet to make the same mistakes that the past Asgardians have made)
Why was the Earth only ready for a higher form of war when S.H.I.E.L.D. used the Tesseract and not Red Skull/Hydra?
First of all, keep in mind that Red Skull failed in his mission. While he did mass produce an arsenal based on the power of the Tesseract, that arsenal was never put to use (other than the showdown in Captain America, which is peanuts compared to the global stage).
Most people are unaware of Red Skull and what he attempted to do, which proves the point that the world is blissfully unaware of this, and therefore their behavior is unchanged.
I can draw an analogy here. Even though nuclear bombs were used in WWII, the Cold War only started when countries started mass producing nuclear weaponry and changing their behavior because they had a sufficient amount of nukes.
I want to pull focus back to Thor's quote:
It is the signal to all the realms that the earth is ready for a higher form of war.
To extend the Cold War analogy, notice that cold wars always happen between countries who both have nuclear weaponry. A country that has no nukes is obviously incapable of partaking in atomic warfare, and it seems commonly accepted that using a nuke against a non-nuclear opponent is unwarranted. There's no point in nuking someone who poses no threat to you.
However, if this country suddenly develops nukes, then they become a viable threat and you will be more inclined to engage them in conflict.
Similarly, humanity now using Tesseract-level weaponry means that they are now open to attack from opponents who wield Tesseract-level weaponry (or different weaponry of a similar level).
Imagine if Captain America looks at what happened in Hiroshima and Nagasaki, and then pensively states the following:
Now that humans have seen the power of atomic weaponry, it is only a matter of time until we start threatening to eradicate people, rather than invade each other's lands to assume control over people.
This is basically what Thor said, but about an even more advanced form of warfare.