How to use controls and the +, ++ notation with Tikz?

Ok, found it.

I wasn't looking at the right place in the manual. Here is the explanation (section 13.4.1 of the manual):

"There is a special situation, where relative coordinates are interpreted differently. If you use a relative coordinate as a control point of a Bézier curve, the following rule applies: First, a relative first control point is taken relative to the beginning of the curve. Second, a relative second control point is taken relative to the end of the curve. Third, a relative end point of a curve is taken relative to the start of the curve."

Too long for a comment

BTW: please always provide self contained full minimal examples, not sniplets like this. Self contained examples are easier to test with.

Here is an example showing there the relative control points are. I'm using polar coords here.

\documentclass[tikz]{standalone}

\usetikzlibrary{decorations.pathreplacing}
\tikzset{%
  show curve controls/.style={
    postaction={
      decoration={
        show path construction,
        curveto code={
          \draw [blue] 
            (\tikzinputsegmentfirst) -- (\tikzinputsegmentsupporta)
            (\tikzinputsegmentlast) -- (\tikzinputsegmentsupportb);
          \fill [red, opacity=0.5] 
            (\tikzinputsegmentsupporta) circle [radius=.2ex]
            (\tikzinputsegmentsupportb) circle [radius=.2ex];
        }
      },
      decorate
}}}


\begin{document}

\begin{tikzpicture}
  \coordinate (A) at (0,0);
  \coordinate (B) at (5,5);
  \draw [show curve controls]
  (A)
  .. controls ++(0:5) and ++ (0:5) ..
  (B)
  ;
\end{tikzpicture}



\end{document}