Americans or British sometimes don't use grammar well. Some particular places include:
--Text messages on phones
--Postings in social media
--When speaking aloud, especially in informal situations.
You are right. These are all correct:
"The government deported a foreign tourist." (Active voice)
"A foreign tourist was deported by the government." (Passive voice).
"A foreign tourist was deported." (Passive voice, so we don't need to say who did it).
"The government deported some foreign tourists."
"Some foreign tourists were deported by the government."
"Some foreign tourists were deported."
A complete, correct sentence would be "American volunteers were deported from Lombok Island."
Headlines often leave out words, abbreviate, use initialisms, or various slang-like words to shorten the headline. This headline is not a complete, correct sentence. It is acceptable as a headline.
You asked the question ".... so Americans or British [people] sometimes don't use grammar well, [isn't] right?"
Well, yes, sometimes - but not in this case.
"American volunteers deported from Lombok island" is not an example of bad English or ungrammatical language. This is not a case of native speakers making the mistake of using an active form when they should be using a passive. Nor is it even a case of native speakers lazily or sloppily dropping important words.
In fact, it is an example of a headline writer using a standard journalistic convention. It is widespread and normal to omit auxiliary verbs and articles from headlines, and the writer here has followed the correct rules of this practice. When we, as native speakers, read this headline we interpret it as 'American volunteers [have been] deported', and we recognise the word 'deported' as a past participle that is part of a passive verb phrase, not a past simple. Then, we move on to read the article itself, we will read this sentence in its full form.