In September 2015, Milla suffered a severe knee injury,[5] returning to action seven months later.[6] On 17 July of the following year, he moved to fellow third division side CF Fuenlabrada also in a temporary deal.[7]
On 11 July 2017, free agent Milla signed a permanent four-year contract with Fuenlabrada.[8] On 28 November, he scored the opener in a 2–2 draw against Real Madrid at the Santiago Bernabéu Stadium, scoring in the stadium 24 years after his father's last goal.[9]
Tenerife
On 19 January 2018, Milla signed a four-and-a-half-year contract with CD Tenerife in Segunda División.[10] He made his professional debut nine days later, playing the full 90 minutes in a 0–0 home draw against Real Valladolid.
Milla scored his first professional goal on 27 October 2018, netting the equalizer in a 3–2 home win against AD Alcorcón. On 24 June 2020, he scored a brace in a 4–1 home routing of CD Mirandés.[11]
Granada
On 31 July 2020, Milla signed a four-year contract with La Liga side Granada CF.[12] On 12 September he marked his competitive debut for his new club and his first appearance in the top division of Spanish football by scoring a goal with a shot from the edge of the area, in a 2–0 victory over Athletic Bilbao.[13]