What you are missing is that as the satellite moves farther away from the Earth, it slows down because of work done by the gravitational field.
Since you have given the satellite more total energy (kinetic plus potential) and because the total energy of a bound orbit is $-GMm/2a$, where $a$ is the semi-major axis, then to increase the energy (make it less negative), $a$ must increase.
For a tangential $\Delta v$, the resulting orbit is an ellipse with a perigee at the point where the velocity was added to the satellite. This is because both energy and angular momentum are conserved - when the satellite returns to the same radius it must have the same tangential velocity (to conserve angular momentum), but then cannot have an extra radial velocity component because that would change the total energy. This is a Hohmann transfer orbit.
On the other hand, a radial impulse adds energy but does not change the angular momentum. The result is an elliptical orbit with a larger $a$, but with a perigee closer to the Earth. The satellite moves outwards first but then falls back. When the satellite returns to the same radius then the tangential part of its velocity must be the same as before the impulse, but to conserve energy there must be an inward radial velocity taking it closer to the Earth. i.e. a more eccentric ellipse is produced than if the same impulse is given tangentially.