Alvarado previously played for the Tampa Bay Rays, having signed there as an international free agent in 2012.

[1] During Alvarado's childhood, Maracaibo was known for its high crime rates, including kidnappings and assault, and he attempted to stay out of trouble while garnering a sense of fearlessness.

[2] The Rays signed him in 2012, as part of an ongoing push from the club to pursue international baseball talent.

In 12 games and 26 innings pitched, Alvarado posted a 2-3 win–loss record with a 3.81 earned run average (ERA) and 20 strikeouts.

[4] In 2015, Alvarado still played in rookie league, and struggled mightily in 5 starts, posting an ERA of 9.53 as he walked 13 batters in 17 innings.

[8] On May 3, 2017, Alvarado was called up directly from Montgomery to give the Rays a left-handed option out of the bullpen, at 21 years of age.

In 2018, Alvarado was a key contributor to the Rays bullpen, specifically in late, high leverage situations.

[10] During the 2019 season, Alvarado struggled with inconsistency and injury, appearing in only 35 games after leaving the United States in June for family reasons,[11] being placed on the 10-day injured list with a right oblique strain, and spending the entire month of September on the injured list with left elbow inflammation.

On the third pitch, Alvarez hit a towering 450 foot shot to center field to give the Astros the lead.

When he returned to the big leagues, he began exclusively using the Cutter as his primary off-speed pitch and abandoned his curveball.