If you use *my value as the search / filter pattern, then it'd 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 filter, you should have your filter text followed by the wildcard, like - my value*.
Further, 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'd search for text beginning with *my value.