Some quick digging shows that those sorts of completions are coming from the PHP.sublime-completions
file. A small excerpt of which is:
{ "trigger": "strncmp", "contents": "strncmp(${1:str1}, ${2:str2}, ${3:len})" },
{ "trigger": "strpbrk", "contents": "strpbrk(${1:haystack}, ${2:char_list})" },
{ "trigger": "strpos", "contents": "strpos(${1:haystack}, ${2:needle})" },
{ "trigger": "strptime", "contents": "strptime(${1:date}, ${2:format})" },
{ "trigger": "strrchr", "contents": "strrchr(${1:haystack}, ${2:needle})" },
{ "trigger": "strrev", "contents": "strrev(${1:string})" },
These completions trigger only for PHP, so a possible problem might be that it doesn’t realize that you’re using PHP (e.g. if you were just entering code in a scratch buffer or something). If that was the case the syntax highlighting would not look right.
Another possibility would be if you have added something (either explicitly or through installing a package on one machine that doesn’t appear on the other) that is overriding this file with one that doesn’t have the completions that you’re interested in.
One other thing that comes to mind (but seems unlikely) would be a key binding issue of some sort; does autocomplete for other languages work or is the problem just restricted to PHP?