Like I've pointed out before, we do not know what Ichigo officially is--same goes for this case. We don't know whether he is a Vizard (Shinji, Kensei, Love, Rose, etc.), Arrancar, both, or something completely different (true hybrid).
Arrancar may enhance their abilities and overall experience in battle, but we've yet to see an overall strength increase and mutation compared to Gillian to Adjuchas (we've yet to see Vasto Lordes). I'm specifically referring to those who've had the Hogyoku used on them. Natural Arrancar have room to improve, sure, but what evolution can be achieved after one is in their purest form? Stay tuned to Bleach for more!
It's obvious his power (or Inner Hollow) grew after his battle with Grimmjow, even after his 'death' to Ulqiuorra--compare their masks. I wouldn't say Ichigo had a battle with Nnoitra, as he pretty much put him his place right after the previous fight--gaining nothing. I suppose you could say the connection with his Inner Hollow grew in the timespan from Grimmjow to Ulqiuorra, as he was able to keep up with him in Bankai when battling unreleased Ulqiuorra then giving him an even better fight with the mask.
However, how did he gain the scarmask? That is the big question here, and only Kubo can officially answer this. That is the point I'm trying to convey here: until then, we do not know. We can only make assumptions, misrepresenting opinions from facts.
Perhaps like zanpakuto, Ichigo's growth as a Hollow increases as a result of embracing Shirosaki--his 'instincts'. Of course, Kubo has yet to clearly define what instincts are in Bleach. He could be referring to what Hollows embody, seeing as how they act on their instinct for hunger and battle to achieve evolution. Once Ichigo truly embraces his 'instincts' then he has full access to his spiritual pressure, abilities, etc. Until then, we just don't know whether Shirosaki acts in the same manner as Menos or something different.
Kubo could be playing around this filler, garnering ideas for upcoming chapters--who knows? In normal cases for filler, they are not valid since they do not hold official connection to the manga--except in certain cases (see Naruto Shippuden).
Like I said earlier, we've yet to see what truly sparked the scarmask. When Kubo decides to officially answer this perhaps we can gain clarity as to what Ichigo is, and how his Inner Hollow evolves and/or what gives Ichigo greater access.