diff --git a/Library/Homebrew/formulary.rb b/Library/Homebrew/formulary.rb
index 9d621eb8f6425..8fd5697067a43 100644
--- a/Library/Homebrew/formulary.rb
+++ b/Library/Homebrew/formulary.rb
@@ -912,7 +912,7 @@ def self.tap_formula_name_path(tapped_name, warn:)
         new_tap = Tap.fetch new_tap_name
         new_tap.ensure_installed!
         new_tapped_name = "#{new_tap_name}/#{name}"
-        name, path = Formulary.tap_formula_name_path(new_tapped_name, warn: false)
+        name, path, tap = Formulary.tap_formula_name_path(new_tapped_name, warn: false)
         old_name = tapped_name
         new_name = new_tap.core_tap? ? name : new_tapped_name
       end
@@ -926,7 +926,7 @@ def self.tap_formula_name_path(tapped_name, warn:)
   def self.tap_loader_for(tapped_name, warn:)
     name, path, tap = Formulary.tap_formula_name_path(tapped_name, warn: warn)
 
-    if name.exclude?("/") && !Homebrew::EnvConfig.no_install_from_api? &&
+    if tap.core_tap? && !Homebrew::EnvConfig.no_install_from_api? &&
        Homebrew::API::Formula.all_formulae.key?(name)
       FormulaAPILoader.new(name)
     else
diff --git a/Library/Homebrew/test/formulary_spec.rb b/Library/Homebrew/test/formulary_spec.rb
index 7c237cc4b429b..9dfe65d4c3d1f 100644
--- a/Library/Homebrew/test/formulary_spec.rb
+++ b/Library/Homebrew/test/formulary_spec.rb
@@ -186,6 +186,48 @@ class Wrong#{described_class.class_s(formula_name)} < Formula
       end
     end
 
+    context "when migrating from a Tap" do
+      let(:tap) { Tap.new("homebrew", "foo") }
+      let(:another_tap) { Tap.new("homebrew", "bar") }
+      let(:tap_migrations_path) { tap.path/"tap_migrations.json" }
+      let(:another_tap_formula_path) { another_tap.path/"Formula/#{formula_name}.rb" }
+
+      before do
+        tap.path.mkpath
+        another_tap_formula_path.dirname.mkpath
+        another_tap_formula_path.write formula_content
+      end
+
+      after do
+        FileUtils.rm_rf tap.path
+        FileUtils.rm_rf another_tap.path
+      end
+
+      it "returns a Formula that has gone through a tap migration into homebrew/core" do
+        tap_migrations_path.write <<~EOS
+          {
+            "#{formula_name}": "homebrew/core"
+          }
+        EOS
+        formula = described_class.factory("#{tap}/#{formula_name}")
+        expect(formula).to be_a(Formula)
+        expect(formula.tap).to eq(CoreTap.instance)
+        expect(formula.path).to eq(formula_path)
+      end
+
+      it "returns a Formula that has gone through a tap migration into another tap" do
+        tap_migrations_path.write <<~EOS
+          {
+            "#{formula_name}": "#{another_tap}"
+          }
+        EOS
+        formula = described_class.factory("#{tap}/#{formula_name}")
+        expect(formula).to be_a(Formula)
+        expect(formula.tap).to eq(another_tap)
+        expect(formula.path).to eq(another_tap_formula_path)
+      end
+    end
+
     context "when loading from Tap" do
       let(:tap) { Tap.new("homebrew", "foo") }
       let(:another_tap) { Tap.new("homebrew", "bar") }