익숙하다 is an adjective, not a verb. Its past tense, 익숙했다 is used when describing the state in the past. For examples, 전에는 익숙했지만 지금은 익숙하지 않아요. 전에는 익숙하지 않았지만 지금은 익숙해요. correction: '익숙해지다'와 ['익숙해졌다'에서도/ 익숙해졌다'는(x)] 같은 질문이 있어요. The verb 익숙해지다 is derived from adjective 익숙하다. Its past tense, 익숙해졌다 is used when descrbing the action in the past. 익숙하다, adjective, to be familar, 익숙하였다 익숙해지다, verb, to be/get accustomed, 익숙해지었다 익숙하게 되다, verb phrase, to become accustomed, 익숙하게 되었다 두 달 동안 한국어를 [공부한/공부하는(x)] 후에 마침내 문장의 끝에 [있는] 동사/형용사를 [보는 것에/보기에] [익숙해졌다/익숙했다(x)]. (After studying Korean for two months, I am finally accustomed to seeing verbs/adjectives at the end of a sentence.) 사실은 (제가 그보다) 더 [오랫동안/ 오래 동안(x)] 한국어를 공부하고 있어요. 예문일 뿐이에요.

현재형 is narrative or descriptive. it has nothing to do with the result of the act. 과거형 emphasizes that the act is completed. for example 익숙하다 means you are familiar with something. 익숙했다 means you were familiar with something. and i think the example you just mentioned used the wrong verb. it should be 두 달 동안 한국어를 공부하는 후에 마침내 문장의 끝에 동사/형용사를 보기에 익숙해졌다. after learning Korean for two months i became accustomed to seeing the verb/adjective at the end of a sentence.