Question: Are both Berberidopsis and Cyclamen genus of flowering plants in the Primulacaea family?

Context articles: Cyclamen (disambiguation)
Echinacea
Magnolia virginiana
Apiaceae
Psychotria
Gnetophyta
Chloranthaceae
Berberidopsis
Cyclamen
Austrobaileyales

Cyclamen is a genus of 23 species of perennial flowering plants in the family Primulaceae.
Echinacea is a genus, or group of herbaceous flowering plants in the daisy family.
 The "Echinacea" genus has nine species, which are commonly called purple coneflowers.
 They are found only in eastern and central North America, where they are found growing in moist to dry prairies and open wooded areas.
 They have large, showy heads of composite flowers, blooming from early to late summer.
 The generic name is derived from the Greek word ἐχῖνος ("ekhinos"), meaning "hedgehog," due to the spiny central disk.
 These flowering plants and their parts have different uses.
 Some species are cultivated in gardens for their showy flowers.
 "Echinacea purpurea" is used in folk medicine.
 Two of the species, "E. tennesseensis" and "E. laevigata", are listed in the United States as endangered species.
Magnolia virginiana, most commonly known as sweetbay magnolia, or merely sweetbay (also laurel magnolia, swampbay, swamp magnolia, whitebay, or beaver tree), is a member of the magnolia family, Magnoliaceae.
 It was the first magnolia to be scientifically described under modern rules of botanical nomenclature, and is the type species of the genus "Magnolia"; as "Magnolia" is also the type genus of all flowering plants (magnoliophytes), this species in a sense typifies all flowering plants.
Apiaceae or Umbelliferae, is a family of mostly aromatic flowering plants named after the type genus "Apium" and commonly known as the celery, carrot or parsley family.
 It is the 16th-largest family of flowering plants, with more than 3,700 species in 434 genera including such well-known and economically important plants such as angelica, anise, asafoetida, caraway, carrot, celery, chervil, coriander, cumin, dill, fennel, hemlock, lovage, cow parsley, parsley, parsnip, sea holly, giant hogweed and silphium (a plant whose identity is unclear and which may be extinct).
Psychotria is a genus of flowering plants in the Rubiaceae family.
 It contains around 1,850 species and is therefore one of the largest genera of flowering plants.
 The genus has a pantropical distribution and members of the genus are small understorey trees in tropical forests.
 Some species are endangered or facing extinction due to deforestation, especially species of central Africa and the Pacific.
Gnetophyta is a division of plants, grouped within the gymnosperms (which also includes conifers, cycads, and ginkgos), that consists of some 70 species across the three relict genera: "Gnetum" (family Gnetaceae), "Welwitschia" (family Welwitschiaceae), and "Ephedra" (family Ephedraceae).
 Fossilized pollen attributed to a close relative of "Ephedra" has been dated as far back as the Early Cretaceous.
 Though diverse and dominant in the Tertiary, only three families, each containing a single genus, are still alive today.
 The primary difference between gnetophytes and other gymnosperms is the presence of vessel elements, a system of conduits that transport water within the plant, similar to those found in flowering plants. Because of this, gnetophytes were once thought to be the closest gymnosperm relatives to flowering plants, but more recent molecular studies have largely disproven this hypothesis.
Chloranthaceae is a family of flowering plants (angiosperms), the only family in the order Chloranthales.
 It is not closely related to any other family of flowering plants, and is among the early-diverging lineages in the angiosperms.
 They are woody or weakly woody plants occurring in Southeast Asia, the Pacific, Madagascar, Central and South America, and the West Indies.
 The family consists of four extant genera, totalling about 77 known species according to Christenhusz and Byng in 2016.
 Some species are used in traditional medicine.
 The type genus is "Chloranthus".
Berberidopsis is a genus of flowering plants in the small family Berberidopsidaceae.
Cyclamen ( or ) is a genus of 23 species of perennial flowering plants in the family Primulaceae.
 Cyclamen species are native to Europe and the Mediterranean Basin east to Iran, with one species in Somalia.
 They grow from tubers and are valued for their flowers with upswept petals and variably patterned leaves.
Austrobaileyales is an order of flowering plants, consisting of about 100 species of woody plants growing as trees, shrubs and lianas.
 Perhaps the most familiar species is "Illicium verum", from which comes the spice star anise.
 The order belongs to the group of basal angiosperms, the ANA grade, which diverged earlier from the remaining flowering plants, and, as such, it is the extant group after the Amborellales and Nymphaeales, that is sister to all remaining extant angiosperms outside of the ANA grade.
 The order includes just three families of flowering plants, the Austrobaileyaceae, a monotypic family containing the sole genus, "Austrobaileya scandens", a woody liana, the Schisandraceae, a family of trees, shrubs, or lianas containing essential oils, and the Trimeniaceae, essential oil-bearing trees and lianas.