The Mindfulness practice that is taught in a secular fashion in the West is based on the Buddhist Satipaṭṭāna-vipassanā practices, but it is a bit different. For one, in Buddhism, vipassnā is meant to be practiced within a certain framework of Buddhist thought and forms only a small part of the overall practice. Second, the "nonjudgemental awareness" you find in secular Mindfulness is something you won't find in the Buddhist Satipaṭṭāna practice. In the discourses the practitioner is instructed direct the mind away from unskillful states and direct the mind towards skillful mental states, so there's definitely an evaluation going on. See Bhikkhu Analayo's "Satipaṭṭāna: The Direct Path to Liberation" text for an in-depth discussion on this.
As a result of the above, the experiences of Mindfulness practitioners can only be loosely connected to what we find in the Buddhist texts. In the discourses, the awareness of impermanence is said to lead to this:
“Bhikkhus, when the perception of impermanence is developed and cultivated, it eliminates all sensual lust, it eliminates all lust for existence, it eliminates all ignorance, it uproots all conceit ‘I am.’" - SN22.102
Buddhist meditators who practice is within the traditional framework certainly experiences these things (it takes a good deal of concentration - i.e. calming of the mind - to get to this point), but do Mindfulness practitioners do as well? And if they do, is that really what they hoped to get out of it?
Most practitioners of Mindfulness do it with the expectation of receiving benefits for their everyday lives. But in Buddhism Satipaṭṭāna practice has usually been the domain of monks and nuns living an ascetic lifestyle. The texts never claim, to my knowledge, that it would make a person more ready to go through the hustle and bustle of a daily layperson's life.
According to Guy Armstrong, a meditation teacher at Spirit Rock, for a while he found that could not relate at all to the Buddhist texts with regard to this meditation practice. But later after his practice deepened and his emotions stabilized, he realized that he was practicing for "emotional healing" but the Buddhist texts were not aimed at that purpose.
So in summary, the secular Mindfulness practice taught in the West today, while having origins in Buddhism, is a 1)slightly different practice and 2)aimed at a different purpose.