Hello! I moved to CA from NY but kept my job in NY and I work remotely (telecommute) from my home. It appears both CA and NY want to tax my wages, is that accurate?

You would file 3 returns:

1. A part-year New York return covering income earned during the time as New York resident (including income from all states during this time period);
2. A part-year California return covering income earned during the time as California resident (including income from all states during this time period);
3. A nonresident New York return covering income earned during the time as California resident (including income earned from New York). 

You should prepare your returns in this order:

1. Nonresident New York (always do any nonresident returns first, so you can get the non-resident state tax credit)
2. Part-year California
3. Part-year New York

Here are more info:
https://ttlc.intuit.com/replies/3302342
https://ttlc.intuit.com/replies/3300295

Why June - September? I moved in April.  When I file as part-year NY they want me to include all of my wages since the source is NY.  Should I not file in CA?

Sorry, that June-September range was for another similar question and was accidentally added here. I have fixed it and the revised answer now addresses your specific situation. Hope this helps!