Small servicers are not exempt from the 120 foreclosure rule you are talking about.
From Regulation X,
1024.41(j): Small servicer requirements. A small servicer shall be subject to the prohibition on foreclosure referral in paragraph (f)(1) of this section. A small servicer shall not make the first notice or filing required by applicable law for any judicial or non-judicial foreclosure process and shall not move for foreclosure judgment or order of sale, or conduct a foreclosure sale, if a borrower is performing pursuant to the terms of an agreement on a loss mitigation option.
1024.41(f)(1): Pre-foreclosure review period. A servicer shall not make the first notice or filing required by applicable law for any judicial or non-judicial foreclosure process unless:
(i) A borrower’s mortgage loan obligation is more than 120 days delinquent;
(ii) The foreclosure is based on a borrower’s violation of a due-on-sale clause; or
(iii) The servicer is joining the foreclosure action of a subordinate lienholder.