Indeed SubstInfinitesimals was provided. That being said the previous input and output whereby its was a list of {0, 0, 0, 0, 0, mathematical expression, mathematical expression } were:
Input: LXi = {r*D[Xi[2][t], t] + Sqrt[r] h[t], Xi[2][t]};
LPhi = {f[r, t] v + g[r, t]};
EDsI = SubstInfinitesimals[EDs, LXi, LPhi]
Output: {0, 0, 0, 0, 0, -r g[r, t] - Sqrt[r] v h[t] - 2 r v Derivative[1][Xi[2]][t] + v \!\(\*SuperscriptBox[\(f\),
TagBox[RowBox[{"(", RowBox[{"0", ",", "1"}], ")"}],Derivative],MultilineFunction->None]\)[r, t] +
\!\(\*SuperscriptBox[\(g\), TagBox[RowBox[{"(", RowBox[{"0", ",", "1"}], ")"}],Derivative],
MultilineFunction->None]\)[r, t] + v \[Rho] \!\(\*SuperscriptBox[\(f\), TagBox[RowBox[{"(", RowBox[{"1", ",", "0"}], ")"}],Derivative],MultilineFunction->None]\)[r, t] - v \[Alpha] \[Lambda][r, t] \!\(\*SuperscriptBox[\(f\), TagBox[RowBox[{"(", RowBox[{"1", ",", "0"}], ")"}],Derivative],
MultilineFunction->None]\)[r, t] + r v \[Beta] \[Lambda][r, t] \!\(\*SuperscriptBox[\(f\), TagBox[
RowBox[{"(", RowBox[{"1", ",", "0"}], ")"}],Derivative],MultilineFunction->None]\)[r, t] + \[Rho]
\!\(\*SuperscriptBox[\(g\), TagBox[RowBox[{"(", RowBox[{"1", ",", "0"}], ")"}],Derivative],
MultilineFunction->None]\)[r, t] - \[Alpha] \[Lambda][r, t] \!\(\*SuperscriptBox[\(g\), TagBox[
RowBox[{"(", RowBox[{"1", ",", "0"}], ")"}],Derivative],MultilineFunction->None]\)[r, t] + r \[Beta] \[Lambda][r, t] \!\(\*SuperscriptBox[\(g\), TagBox[RowBox[{"(", RowBox[{"1", ",", "0"}], ")"}],Derivative],
MultilineFunction->None]\)[r, t] + 1/2 r v \[Sigma]^2 \!\(\*SuperscriptBox[\(f\), TagBox[RowBox[{"(",
RowBox[{"2", ",", "0"}], ")"}],Derivative],MultilineFunction->None]\)[r, t] + 1/2 r \[Sigma]^2
\!\(\*SuperscriptBox[\(g\), TagBox[RowBox[{"(", RowBox[{"2", ",", "0"}], ")"}],Derivative],MultilineFunction->None]\)[r, t], -((\[Rho] h[t])/( 2 Sqrt[r])) + (\[Sigma]^2 h[t])/(
8 Sqrt[r]) + (\[Alpha] h[t] \[Lambda][r, t])/(2 Sqrt[r]) + 1/2 Sqrt[r] \[Beta] h[t] \[Lambda][r, t] -
Sqrt[r] Derivative[1][h][t] + r \[Beta] \[Lambda][r, t] Derivative[1][Xi[2]][t] -
r (Xi[2]^\[Prime]\[Prime])[t] - \[Alpha] Xi[2][t] \!\(\*SuperscriptBox[\(\[Lambda]\),TagBox[RowBox[{"(",
RowBox[{"0", ",", "1"}], ")"}],Derivative],MultilineFunction->None]\)[r, t] + r \[Beta] Xi[2][t]
\!\(\*SuperscriptBox[\(\[Lambda]\), TagBox[RowBox[{"(", RowBox[{"0", ",", "1"}], ")"}],Derivative],
MultilineFunction->None]\)[r, t] + r \[Sigma]^2 \!\(\*SuperscriptBox[\(f\), TagBox[RowBox[{"(",
RowBox[{"1", ",", "0"}], ")"}],Derivative],MultilineFunction->None]\)[r, t] - Sqrt[r] \[Alpha] h[t]
\!\(\*SuperscriptBox[\(\[Lambda]\), TagBox[RowBox[{"(",RowBox[{"1", ",", "0"}], ")"}],Derivative],
MultilineFunction->None]\)[r, t] + r^(3/2) \[Beta] h[t] \!\(\*SuperscriptBox[\(\[Lambda]\), TagBox[
RowBox[{"(", RowBox[{"1", ",", "0"}], ")"}],Derivative],MultilineFunction->None]\)[r, t] - r \[Alpha] Derivative[1][Xi[2]][t] \!\(\*SuperscriptBox[\(\[Lambda]\), TagBox[RowBox[{"(", RowBox[{"1", ",", "0"}], ")"}],Derivative],MultilineFunction->None]\)[r, t] + r^2 \[Beta] Derivative[1][Xi[2]][t]
\!\(\*SuperscriptBox[\(\[Lambda]\), TagBox[RowBox[{"(",RowBox[{"1", ",", "0"}], ")"}],Derivative],
MultilineFunction->None]\)[r, t]}
Hope this is clearer.