 He also made 6 appearances in European competition for Dundalk against AFC Ajax in the 1987–88 European Cup Winners' Cup, against Red Star Belgrade in the 1988–89 European Cup and Budapest Honvéd FC in the 1991–92 European Cup.In the 1990-91 League of Ireland season Eviston was everpresent in the league scoring 10 goals as Dundalk won the league on the last day at Cork with Eviston playing a role in Tom McNulty's winner.He rejoined Rovers in the summer of 1993 and scored 6 goals in 25 appearances as he picked up his fourth League medal in his first season back in the Hoops.