There are actually two issues here: (1) you are not prohibited from working as a Mental Heath provider if you weren't convicted of Assault, BUT (2) An employer can chose not to hire you based on any criminal conviction.
If you were offered the job, then they probably already know abut the conviction and don't care. So why worry? If they offered you the job and then withheld it after running a background check, employers have wide discretion to hire or not to hire based on a person's criminal history.
Domestic violence assault is just regular, simple assault, with an added element that the assault had to take place against a family member as defined by statute. The consequences are more severe in that any domestic violence conviction comes with a surrender of firearm rights.
Domestic Violence Assault 4 is actually more serious that a simple Assault 4. When a charge is designated as Domestic Violence under RCW 10.99, it carries collateral consequences that include but are not limited to, ineligibility to possess firearms, 1 year of domestic violence treatment, No Contact Order with the alleged victim, and no possibility of vacating/ expunging the charge from your record. It can also bar you from specific areas of employment and housing.
Neither a simple assault 4 or a disorderly conduct on the other hand carry the same ramifications. However, in a competitive job market, a criminal charge of any kind can reduce your chances of getting hired if there are other applicants similarly qualified without any criminal history. In this case, if a conviction for disorderly conduct is listed as an offense that would bar you from employment, you are probably ok.
If you do find that you are being denied employment, you may want to consider is getting a copy of your criminal record to insure that it is being reported accurately. I have come across cases where a charge was amended but records indicated a conviction on the original charge. In one case, I had a client who was turned down for multiple jobs because she had a felony on her record. As it turns out she had been charged with robbery but that charge was later amended to a theft 3rd. Yet her record showed a conviction for the robbery. It was just a clerical error and was easy to fix once we knew about it.