Some players only score a lot of goals at one club in their career when things align for them in terms of manager, tactics and teammates.
They struggle when they leave for another club (e.g. Ian Rush and Luther Blissett when they went to Italy)
Burns looks to be one of those.
I don't know if he'll recapture that old Phoenix form under a different manager - at least a handful of the players are the same (Krishna, Wee Mac, Durante, Doyle). There's also his long history of injuries to consider (Burns has only played 128 league games in his 12 year senior career).
If you look at his career stats outside that one season with the Phoenix, its not impressive:
https://us.soccerway.com/players/nathan-burns/1749...
https://www.transfermarkt.com/nathan-burns/leistun...
https://www.transfermarkt.com/nathan-burns/detaill...
http://www.ultimatealeague.com/player_detail.php?p...
(The sites above are incomplete but you can work out career stats from them together)
League games (not including cup games):
Phoenix 2014-15: 24 apps 13 goals 6 assists
AEK Athens (Greek Super League) 2008-12 : 21 apps 1 goal 1 assist
AOK Kerkyra (Greek second tier) 2009-10; 31 apps 8 goals 0 assists
FC Tokyo 2015-17: 26 apps 3 goals 6 assists
Newcastle Jets A-League 2013-14 12 apps 2 goals 0 assists
Adelaide United 2006-08: 35 apps 9 goals
Total games and goals excluding his previous brilliant season with the Nix (adding 3 apps for Incheon in the K-League where he filed to score): 128 league games 23 goals