How is the law applicable for filing a civil action against an agency in another state?

If a person has a contract with an agency in California and the contractor's residence and place of work is in Washington state, can the contractor file a civil action against the agency in Washington? It is good to say that in the contract itself indicates "the agreement is executed in California and shall be construed and enforced in accordance with the state law". But civil action is not about the contract itself, it is about some extra promises and expenses that just were exchanged by Emails and verbal words.

Overall, do I need to go to California to pursue the matter or just in Washington state I can initiate the class action?

No, you cannot initiate in Washington. Your collateral agreement is still bound to the terms of the contract itself which states you must sue in California and apply California law.