If you use *my value as the search / filter pattern, then it would mean anything in the beginning and must have my value in the end. So, it is being interpreted correctly as Ends With.
If you want to have a Begins With the filter, have your filter text followed by the wildcard, like - my value*.
If you want to include wildcard as a literal in the search pattern, you'd need to escape that by enclosing it in brackets like [*]my value* - this search for text beginning with *my value.