Yup. Linking is not that easy.
Most basic Akuma combo is close HP, LK Tatsu, HP Shoryu. That one is a cancel because the close HP is actually negative frame recovery on hit, but you can cancel into the Tatsu (or another special) at anytime during the hitstun to skip the recovery so that it will combo.
Not everything can be done like this. Only your light attacks can cancel into each other like this. Mash crouch jab x3 and it will easily string together; despite the frame advantage on the first jab being good, the second will still cancel out of the hitstun of that without the need for a proper recovery.
Linking is different. You cannot cancel a cr.MP into a second cr.MP during the hitstun in that way, and you also cannot cancel a cr.LP into a cr.MP or vice versa.
For linking; when a move gives you +5 frame advantage on hit for example, you link by squeezing a move of 5 frame startup or less into that window of frame advantage. The quicker the speed of your linking normal, the easier it can be to time correctly. Unlike with chaining, if you input your link too early (before your last normal fully recovered), the normal will simply not come out; whereas if you input your normal too late, it will come out but will not combo correctly.
Once you link correctly your normal will be a stand-alone attack despite being combo’d into and will allow you to cancel into your special as with the example of close HP. There’s a difference with chains so that these combos aren’t some dumb easy mode. If you chain your 3 light normals together, the ability to cancel your last light into a special is removed and try as you might; you’ll just get a standing light kick instead of the Tatsu.
What has to be done for this combo to work is to link into your last jab after the first two are chained so that it’s considered a stand-alone light. Thing is that if you jab just one frame before the previous jab fully recovered it will chain again and cut your combo. I recommend linking to cr.MP after your first two jabs instead. It’s a 4 frame startup instead of 3 so there’s only a 1 frame difference, you dont get the same problem you would with a third jab and the combo will do more damage since a linked cr.MP does at least twice the base damage of a linked jab.
Jab x3 into Tatsu isnt really a basic combo, it has execution requirements that make it worthy of a hard trial.
Developing links is just a matter of repeating practice and gradually programming the correct timing for the input. The double roundhouse gives you +5 on hit and the cr.MK you are trying to link with is 5 frames, so your timing has to be absolutely spot-on. cr.LK and cr.MP are both good 4 frame links with best reach for the roundhouse follow-up. cr.LK is the most consistent since it doesn’t pushback on hit, but it does crap damage as a linked normal. cr.MP pushes back a little but does the same damage as a cr.MK.
Either get started with linking the roundhouse to the combo with cr.MP for strong damage, or start with cr.LK as a beginner and upgrade when you are comfortable with the link. cr.LP gives you yet more leniency with link timing, but with its short reach; a link into a roundhouse combo will only be possible from hitting the roundhouse at a specific close range.