I'm surprised this hasn't been mentioned already, but one thing I've found mentioned again and again in various meditation forums as an aid for people struggling with difficult feelings brought up by meditation is "metta" meditation, which translates roughly to "loving-kindness". Through one way or another (often repeated mantras are used), the meditation aims to generate feelings of love and goodwill towards both the meditator and towards others. This compassion can then be called on if difficult feelings arise (and my understanding is they often do at some point).
My understanding is that insight meditation practices in particular, like Vipassana mentioned in the article, are especially likely to bring up difficult feelings. But if one has some sort of "safe container" they can put those feelings within, then they have the opportunity to integrate the experience, and they can grow from that. It's much like being able to recount a traumatic experience in a setting where you feel safe and listened to; it can allow for real healing. But there _needs_ to be some safe context for the pain to be felt. I feel like I read a lot of stories about people trying to dig up as much "insight" as they can, but without giving thought to how they might be able to integrate them (both with meditation and also psychedelics).
For anyone interested in this stuff, I've found Radical Self Acceptance by Tara Brach to be a really great source of both guided metta meditations as well as discussions about balancing "Seeing"/"Insight" and having the safe emotional container for experiences. I would also highly recommend The Mind Illuminated, mentioned elsewhere in this thread, as a great general textbook on meditation, which also gives special attention to uncovering Insight in a way that can be safely integrated.