TikZ nested text boxes margins

An alternative solution with a matrix of nodes. A matrix is a node which contains other nodes, therefore, the outer node can be filled with blue color, and inner nodes with its own color, blue for top most nodes and orange for others.

documentclass[tikz, border=2mm]{standalone}
usepackage{tikz}
usetikzlibrary{matrix}

begin{document}

definecolor{CoreBlue}{HTML}{5b9bd5}
definecolor{CoreOrange}{HTML}{ec7d2d}

tikzset{
    Core/.style={matrix of nodes, draw=CoreBlue, fill=CoreBlue, text=white,
        nodes={anchor=center, text width=17mm, align=center, fill=CoreOrange, draw=CoreOrange},
        row 1/.style={nodes={fill=CoreBlue, draw=CoreBlue}}},
}

begin{tikzpicture}[]
  matrix[Core] {Lorem \
     {scriptsize Ipsum}\};
end{tikzpicture}

end{document}

This is a simple and quick solution/suggestion: use minimum width,minimum height, text width, and align=center. You may make a newcomnand to fit your need. The above Zarko's answer has some advantage over mine.

documentclass[tikz,border=2mm]{standalone}
usepackage{lipsum}
begin{document}
definecolor{CoreBlue}{HTML}{5b9bd5}
definecolor{CoreOrange}{HTML}{ec7d2d}
begin{tikzpicture}
path 
(0,0) node[fill=CoreBlue,minimum width=30mm,minimum height=12mm] (A) {}
(A.center)+(90:3mm) node[text=white] {Lorem}
(A.center)+(-90:2mm) node[fill=CoreOrange,text=white,minimum width=25mm,text width=20mm,align=center,font=scriptsize]{Ipsum};
end{tikzpicture}
end{document}

To long for the comment:

• Don't nest TikZ pictures!
• One of possibilities for your node is

documentclass[tikz, border=2mm]{standalone}
usetikzlibrary{backgrounds, 
                fit,
                positioning,
                shapes.multipart}
definecolor{CoreBlue}{HTML}{5b9bd5}
definecolor{CoreOrange}{HTML}{ec7d2d}
begin{document}
tikzset{
    base/.style = {text width=#1, align=center, text=white, outer sep=0pt},
    base/.default = 17mm,
      CB/.style = {base=#1, fill=CoreBlue},
      CO/.style = {base=#1, fill=CoreOrange},
        }
begin{tikzpicture}[]
  node (1a) [CB] {Lorem};
  node (1b) [CO,below=0mm of 1a] {Ipsum}; \
scoped[on background layer]
  node (1)  [CB, fit=(1a) (1b)] {};
end{tikzpicture}
begin{tikzpicture}[]
  node (1a) [CB] {Lorem};
  node (1b) [CO,below=0mm of 1a] {Lorem Ipsum}; \
scoped[on background layer]
  node (1) [CB, fit=(1a) (1b)] {};
end{tikzpicture}
end{document}

or

documentclass[tikz, border=2mm]{standalone}
usetikzlibrary{backgrounds, 
                fit,
                positioning,
                shapes.multipart}
definecolor{CoreBlue}{HTML}{5b9bd5}
definecolor{CoreOrange}{HTML}{ec7d2d}

usepackage{lipsum}
begin{document}
tikzset{
    base/.style = {text width=#1, align=center, text=white, outer sep=0pt},
    base/.default = 21mm,
      CB/.style = {base=#1, fill=CoreBlue},
      CO/.style = {base=#1, fill=CoreOrange, font=scriptsize},
        }
begin{tikzpicture}[]
  node (1a) [CB] {Lorem};
  node (1b) [CO,below=0mm of 1a] {Ipsum}; \
scoped[on background layer]
  node (1)  [CB, fit=(1a) (1b)] {};
end{tikzpicture}
begin{tikzpicture}[]
  node (1a) [CB] {Lorem};
  node (1b) [CO,below=0mm of 1a] {lipsum[1][1]}; \
scoped[on background layer]
  node (1) [CB, fit=(1a) (1b)] {};
end{tikzpicture}
end{document}

I suggest to draw it directly rather than nested node. If they are repeated in your code, put it in a pic.

documentclass[tikz, border=2mm]{standalone}
usepackage{tikz}
usetikzlibrary{fit, positioning, backgrounds}

begin{document}

definecolor{CoreBlue}{HTML}{5b9bd5}
definecolor{CoreOrange}{HTML}{ec7d2d}

tikzset{
    Core/.style={rectangle, draw, fill=CoreBlue,  draw opacity=0, text=white},
    Core2/.style={rectangle, draw, fill=CoreOrange,  draw opacity=0, text=white},
}

begin{tikzpicture}
  defpadwidth{2mm}
  node[Core2,align=center,text width=15mm] (a) {scriptsize Ipsum};
  path ([xshift=-padwidth]a.west) coordinate (a-l)
    ([xshift=padwidth]a.east) coordinate (a-r);
  node[above=0pt of a] (b) {Lorem};
  pgfkeysgetvalue{/pgf/inner ysep}wrapnodetbsep
  path ([yshift=-wrapnodetbsep]a.south) coordinate (a-b);
  scoped[on background layer] node[fit=(a)(b)(a-l)(a-r)(a-b), inner sep=0pt, fill=CoreBlue] {};
end{tikzpicture}

end{document}