Kunyora kuenderera mberi kweiyi ndima - Kudzokera kuNorth America, Jokinen akatanga mwaka wa1998-1999 neAmerican Hockey League (AHL) yakabatana neKings, iyo Springfield Falcons. Akawana kudana kuLos Angeles mushure memitambo mipfumbamwe, umo akawana pfungwa pfumbamwe. Akanyora pfungwa yake yekutanga yeNHL musi waNovember 5, 1998, aine rubatsiro mumutambo wakanangana neSt. Louis Blues, ndokuzonyora chinangwa chake chekutanga cheNHL masikati mashanu gare gare kurwisa Calgary Flames. Jokinen akatumidzwa zita rekuti NHL's Rookie of the Month for November, achiwana mapoinzi masere mumitambo gumi nerimwe. Akapedza mwaka aine mapoinzi makumi maviri nerimwe mumitambo makumi matanhatu nenomwe. Kutevera kupera kwemwaka, musi waJune 20, 1999, Jokinen akatengeswa kuNew York Islanders, pamwe naJosh Green, Mathieu Biron uye sarudzo yekutanga yegore iroro.
, mukutsinhana naŽigmund Pálffy, Bryan Smolinski, Marcel Cousineau uye sarudzo yechina. Jokinen aionekwa sechikamu chikuru chechibvumirano kubva pakuona kweNew York, sezvo vakasiya mutambi wavo wepamusoro muPálffy.