Native language speakers, especially ESL teachers, quickly learn to identify non-native speakers. Accent is less important than what is termed translation errors, meaning structures translated literally from the speaker’s native tongue.
A classic Hebrew speaker mistake is the use of the future tense in temporal clauses, i.e. after the words when, after, as soon as, etc. Hebrew is a quite straight forward language regarding tenses. When the meaning is in the future, you put the verb in the future. By contrast, English avoids use of the future tense as much as possible, almost entirely limiting to the use in the independent clause, the main verb in the sentence. Dependent parts are assumed to be in the same tense as the main verb and are thus written in the present simple. Native speakers take this fact for granted, but English as a second language speakers often struggle with this tendency.
For example, in Hebrew, one would write .כאשר אבין את המאמר הזה, אסביר לך, with the two underlined verbs in the future, as compared to the English version: When I understand this article, I will explain it to you. The independent part of the sentence is the future, making it obvious that the whole sentence is in the future.
Isn’t that clear?