The problem is that the boxchart function doesn't work well within a tiled layout. However, you can use the boxplot function instead, which works fine within a tiled layout.
tiledlayout('flow');
clear color
%preallocate an array of colors with NaN
color = NaN(length(double(type)), 3);
for i = 1:npeople
[colorinx,tf] = listdlg('PromptString', append('Select the files for participant ', num2str(i)), 'SelectionMode','multiple','ListString',rownames, 'ListSize', [300 200]);
%list of possible colors
colors = {'red'; 'green'; 'blue'; 'magenta'; 'yellow'; 'black'};
%assign the colors a color code
colorCodes = [[1 0 0]; [0 1 0]; [0 0 1]; [0 1 1]; [1 0 1]; [1 1 0]; [0 0 0]];
coloroption = listdlg('PromptString', 'Select color for this participant', 'SelectionMode','multiple','ListString',colors, 'ListSize', [300 200]);
%match the colors selected with their color code
color(colorinx,:) = colorCodes(coloroption,:).*ones(size(color(colorinx,:)));
end
%for loop that changes PSD values being plotted
for i = 1:5
%make the grouping column (cond) numerical so that it can be used in scatterplot
type = renamecats(categorical(cond), {'condition x', 'condition y'}, {'1','2'});
%make a boxplot based on the conditions and all of the points
nexttile
hold on
boxplot(PSD(points,i), type, 'Colors', 'k', 'Symbol', '');
ylabel('PSD (%)')
xlabel('Condition')
%overlay the scatterplot onto the boxplot made earlier
scatter(double(type), PSD(points,i), 25, color, 'filled', 'XJitter', 'rand', 'XJitterWidth', 0.3)
end
