The right-hander spent a season at junior college then made his pro debut in 1997 with the AZL Mariners (1–0, Sv, 4.17, 50 K, 6 BB in 451⁄3 IP) and Everett AquaSox (2.08 in 2 G).
The right-hander returned to the AZL Mariners for '98 and went 3–0 with a 2.20 ERA in 17 games, fanning 51 batters in 41 innings while giving up just 29 hits.
In 1999, the Mayagüez native became a starter and was 9–9 with a 4.63 ERA for the Wisconsin Timber Rattlers; he struck out over 3 times as many as he walked and averaged nearly a K per inning.
He returned in 2002 to pitch for the San Antonio Missions (1–0, 4.91 in 3 G) and Tacoma Rainiers (4–7, 5.92, .300 average allowed), struggling in his AAA debut.
In the winter of 2004–2005, Josue went 5–2 with a 2.63 ERA for the Gigantes de Carolina; he tied Evan Thomas and Jonathan Albaladejo for the Puerto Rican League lead in victories.
Matos pitched for Puerto Rico in the 2005 Baseball World Cup but went 0–3 with a 4.76 ERA, losing to Team USA, Japan and Australia.
He then won his only appearance in the 2009 Caribbean Series, tossing 5 shutout innings of 2-hit ball but walking six Licey Tigers.