Description:
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From manual page: https://php.net/datetime.formats.relative
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What is missing is the following paragraph:

"The referent of the reltext keywords depend on the context in which the relative format string is used. If used with a static method or function, the referent is the current system timestamp. However, if used in DateTime::modify() or DateTimeImmutable::modify(), the referent is the object on which the modify() method is called."

Thank you! 

Test script:
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<?php
header("Content-Type: text/plain");
$thisMonthDateTime = date_create("first day of this month");
echo $thisMonthDateTime->format("Y-m-d") . "\r\n";
$januaryDateTime = DateTime::createFromFormat("Y-m-d", "2019-01-15");
$januaryDateTime->modify("first day of this month");
echo $januaryDateTime->format("Y-m-d");

Actual result:
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The two displayed dates are different, AS THEY SHOULD BE. What is missing is DOCUMENTATION of the behavior.