At club level, Rubio began his professional career with Murcielagos F.C. in 2015 in the Ascenso MX, also later playing for Murcielagos in Liga Premier before moving to USL Championship with Tacoma Defiance in 2019 and Switchbacks in 2020. He then joined AD Chalatenango in early 2021 while the USL Championship 2021 season was on hold due to the Covid-19 pandemic.

Rubio began his professional career as a defensive-minded left-back, but later made his name as an aggressive, courageous, physical, and hard-tackling centre-back, with a penchant for scoring headers from set-pieces, due to his aerial prowess and strength. A versatile, consistent, commanding, and dependable left-footed defender, with good awareness, positional sense, and an ability to read the game, he is capable of playing both in a three or four-man defence. A hard-working player, he is also known for his ability to cover ground and put pressure on or anticipate opponents in positions higher up on the pitch. Due to his tenacious, no-nonsense playing style, Rubio can be described as an "old-fashioned" centre-back, who primarily serves as a ball-winner; his physicality and aggression as a defender, have earned him the nickname "Mexican Chiellini", in honor of Italian left footer centre-back Giorgio Chiellini. A mobile defender, he possesses good vision and reliable distribution, which allows him to play the ball out or launch attacks from the back after winning back possession. Moreover, he possesses a strong mentality, good temperament under pressure, determination, and excellent concentration.