Genearlly, when you enter into US while working for a Cdn firm, you enter on B1 business status. Cdns enter without a visa, but you will probably need a consular visa, unless your country is part of VWP and you enter for less than 90 days at a time.
Ecuador is not part of VWP, so you will need a visa.
Not all work can be done under B1, but this work appears to satisfy the requirements.
I have no idea what
mexico would need.
Your firm should be handling this.