What is it that you don't understand? That's the most effective exercise for getting the ear in the right shape, even more effective than eartune. But yeah it sounds like your hearing the right things in the notes themselves. Do you have to try to listen or can you perceive it naturally? If you find yourselve trying to hear something then you should do more exercises. Here's one that goes with something your already doing.

When you play your Jazz chords, and say it's 3 notes. Play it and try to listen for each note in the chord. So if you play a C major chord (x320xx), listen for C, then E, then G. Say your listening for E. When you think you have it, mute the guitar, and try to hum the note (from memory), then play E over what your humming to check yourself. If you can master this exercise, then your ear will start to perceive the colors more vividly without you even having to try.

Ear training

Sounds good. One thing that will help is try going through eartune before you go to bed. Just for a few minutes as sort of a refresher. Watch adding other instruments. If you rush or try to do too much, you won't get it, trust me. You should at least be able to get 95+ out of a hundred, before adding another note to eartune. Absolute pitch has more to do with hearing a pitch than recognizing it, recognizing comes naturally and will stick with you for the rest of your life only after you can hear each pitch vividly. So you don't want to add notes until you feel as comfortable naming these pitches as naming the colors of the color palette. So use good judgement before you decide to take another step.

Last question: To learn how to learn a solo or a song by ear: Is it enough if I work on with Eartune?

Yes, any ear training will definitely help with learning songs and solo's by ear. But developing this skill only comes when you practice this skill. Figuring out as many songs as you can on your own is the best way to accomplish your goal in this area. Ear training will speed up the process and make it easier, but you still have to do the skill. There is software out there to slow down music to aid you, so check that out.