PS doesn't know anything about the specific physical and chemical properties of different inks like pigment density, viscosity etc. that would determine the actual print appearance, so there can be no automatic compensation. That's what colro profiles are for - or, as you already figured, you have to create your own manual adjustments.
I would also be concerned with color-fastness of off-brand inks. Are they fade resistant over time like many name-brand inks are now? What archival longevity specs does Dealo provide with the paper you are using? Does Dealo provide profiles for thier product specific to your printer and the paper you are using. What about metameric issues? - where certain colors can visually change depending on the spectra of the light source they are viewed under.
I agree name brand inks are astronomically overpriced. But for work I sell to clients, there are many important considerations besides the cost of the ink.
The main thing you have to change with generic inks is your expectation of quality and consistency over time.
You could have a custom profile made for your specific combination of printer/paper/ink, but there's no guarantee the custom profile will work with the next batch of inks you use.